Question 12 Marks
Simplify : $a^2 − 2a + {5a^2 − (3a + 4a^2)}$
Answer$= a^2 − 2a + {5a^2 − 3a + 4a^2}$
$= a^2− 2a + {9a − 3a}$
$= a^2− 2a + 9a^2 − 3a$
$= 10a^2 − 5a$
View full question & answer→Question 22 Marks
Divide : $ 8x − 10y + 6c by 2$
Answer$ \frac{8 \mathrm{x}-10 \mathrm{y}+6 \mathrm{c}}{2}$
$ =\frac{8 \mathrm{x}}{2}-\frac{10 \mathrm{y}}{2}+\frac{6 \mathrm{c}}{2}$
$ =4 \mathrm{x}-5 \mathrm{y}+3 \mathrm{c}$
View full question & answer→Question 32 Marks
Divide : $63\ a^4b^5c^6 by −9\ a^2b^4c^3$
Answer$\frac{63 a^4 b^5 c^6}{-9 a^2 b^4 c^3}=\left(\frac{63}{-9}\right)\left(\frac{a^4}{a^2}\right)\left(\frac{b^5}{b^4}\right)\left(\frac{c^6}{c^3}\right)$
$=-7 \ a^{4-2} \cdot b^{5-4} \cdot c^{6-3}$
$=-7 \ a^2 b c^3$
View full question & answer→Question 42 Marks
Divide: $−24x^4d^3 by −2x^2d^5$
Answer$ \frac{-24 x^4 d^3}{-2 x^2 d^5}=\left(\frac{-24}{-2}\right)\left(\frac{x^4}{x^2}\right)\left(\frac{d^3}{d^5}\right) $
$ =12 x^{4-2} d^{3-5} $
$=12 x^2 d^{-2} $
$ =\frac{12 x^2}{d^2}$
View full question & answer→Question 52 Marks
Divide: $24x^3y^3 by −8y^2$
Answer$\frac{24 \mathrm{x}^3 \mathrm{y}^3}{-8 \mathrm{y}^2}=\left(\frac{24}{-8}\right)\left(\mathrm{x}^3\right)\left(\frac{\mathrm{y}^3}{\mathrm{y}^2}\right)$
$=-3 x^3 y^{3-2}$
$==-3 x^3 y$
View full question & answer→Question 62 Marks
Divide: $−70a^3$ by $14a^2$
Answer$ \frac{-70 \mathrm{a}^3}{14 \mathrm{a}^2}=\left(\frac{-70}{14}\right)\left(\frac{\mathrm{a}^3}{\mathrm{a}^2}\right) $
$ =-5 \mathrm{a}^{3-2} $
$ =-5 \mathrm{a}$
View full question & answer→Question 72 Marks
Simplify : $(4x – 5y) (5x – 4y)$
Answer$(4x – 5y) (5x – 4y)$
$= 4x(5x – 4y) – 5y(5x – 4y)$
$= 20x^2 – 16xy – 25xy + 20y^2$
$= 20x^2 – 41xy + 20y^2$
View full question & answer→Question 82 Marks
Simplify : $(px – q) (px + q)$
Answer$(px – q) (px + q) = px(px + q) – q(px + q)$
$= p^2x^2 + pxq – pqx – q^2$
$= p^2x^2 – q^2$
View full question & answer→Question 92 Marks
Simplify : $(7x – 8) (3x + 2)$
Answer$(7x – 8) (3x + 2) = 7x(3x + 2) −8(3x+ 2)$
$= 21x^2 + 14x – 24x – 16$
$= 21x^2 – 10x – 16$
View full question & answer→Question 102 Marks
Multiply: $3-\frac{2}{3} x y+\frac{5}{7} x y^2-\frac{16}{21} x^2 y$ by $-21 x^2 y^2$
Answer$=63 x^2 y^2+\frac{42}{3} x^3 y^3-\frac{105}{7} x^3 y^4+16 x^4 y^3$
$ =-63 x^2 y^2+14 x^3 y^3-15 x^3 y^4+16 x^4 y^3$
View full question & answer→Question 112 Marks
Multiply: $5x^2- 8xy + 6y^2 - 3by - 3xy$
Answer$5x^2- 8xy + 6y^2 - 3by - 3xy$
$= (5x^2 - 8xy + 6y^2 - 3)(-3xy)$
$= -15x^3y + 24x^2y^2− 18xy^3+ 9xy$
View full question & answer→Question 122 Marks
Multiply: $(ab – 1) (3 – 2ab)$
Answer$(ab – 1) (3 – 2ab)$
$ab(3 − 2ab) − 1(3 − 2ab)$
$3ab − 2a^2b^2 − 3 + 2ab$
$5ab − 2a^2b^2 − 3$
View full question & answer→Question 132 Marks
Evaluate: $2x(3x – 5) – 5(x – 2) – 18$ for $x = 2.$
AnswerFor $x = 2$
$2\times(3x – 5) – 5(x – 2) – 18$
$2 \times 2(3 \times 2 − 5) − 5(2 − 2) − 18$
$4(6 − 5) − 5 \times 0 − 18$
$4 − 18$
$= − 14$
View full question & answer→Question 142 Marks
Evaluate: $xy^2(x – 5y) + 1$ for $x = 2$ and $y = 1.$
AnswerFor $x = 2$ and $y = 1$
$xy^2(x – 5y) + 1$
$2 \times 1^2(2 − 5 \times 1) + 1$
$2 \times (2 − 5) + 1$
$2 \times (−3) + 1$
$= −5$
View full question & answer→Question 152 Marks
Evaluate: $x(x – 5) + 2$ for $x = 1.$
AnswerFor $x = 1$
$x(x – 5) + 2$
$1(1 − 5) + 2$
$−4 + 2$
$= −2$
View full question & answer→Question 162 Marks
Multiply: $x^2+ x + 1$ by $1 − x$
Answer$(x^2+ x + 1) (1 − x) $
$= 1(x^2 + x + 1) − x(x^2 + x + 1)$
$= x^2+ x + 1 − x^3 − x^2 − x$
$= 1 − x^3$
View full question & answer→Question 172 Marks
Multiply: $-\frac{3}{2} x^5 y^3$ and $\frac{4}{9} a^2 x^ 3 y$
Answer$ \left(-\frac{3}{2} x^5 y^3\right)\left(\frac{4}{9} a^2 x^3 y\right)$
$ =\left(-\frac{3}{2} \times \frac{4}{9}\right)\left(a^2\right)\left(x^5 \times x^3\right)\left(y^3 \times y\right)$
$ =\frac{-2}{3} a^2 x^8 y^4$
View full question & answer→Question 182 Marks
Multiply: $−3bx, −5xy$ and $−7b^3y^2$
Answer$−3bx \times −5xy \times −7b^3y^2$
$= (−3 \times −5 \times −7)(b \times b^3) (x \times x)(y \times y^{2)}$
$= −105\ b^4x^2y^3$
View full question & answer→Question 192 Marks
Evaluate: $xz (x^2 + y^2)$ for $x = 2, y = 1$ and $z= 1.$
AnswerFor $x = 2, y = 1$ and $z = 1$
$xz (x^2 + y^2)$
$2(1) \times (2^2 + 1^2)$
$2 \times (4 + 1)$
$2 \times 5$
$= 10$
View full question & answer→Question 202 Marks
Multiply: $abx, −3a^2x$ and $7b^2x^3$
Answer$abx \times −3a^2x \times 7b^2x^3$
$= (−3\times 7) (a \times a^2) (b \times b^2) (x \times x \times x^3)$
$= −21a^3b^3x^5$
View full question & answer→Question 212 Marks
Multiply: $a^2, ab$ and $b^2$
Answer$a^2 \times ab \times b^2$
$= a^{2+1}. b^{1+2}$
$= a^3b^3$
View full question & answer→Question 222 Marks
Multiply: $12a + 5b$ by $7a − b$
Answer$(12a + 5b) (7a − b) = 12a (7a − b) + 5b (7a − b)$
$= 84a^2 − 12ab + 35ab − 5b^2$
$= 84a^2 + 23ab − 5b^2$
View full question & answer→Question 232 Marks
Multiply: $5a − 1$ by $7a − 3$
Answer$(5a − 1)(7a − 3)$
$= 5a (7a − 3) − 1 (7a − 3)$
$= 35a^2 − 15a − 7a + 3$
$= 35a^2 − 22a + 3$
View full question & answer→Question 242 Marks
Multiply: $x + 4$ by $x − 5$
Answer$(x + 4)( x − 5) $
$= x( x − 5) + 4(x − 5)$
$= x^2 − 5x + 4x − 20$
$= x^2 − x − 20$
View full question & answer→Question 252 Marks
Multiply: $2a^2 − 5a − 4$ and $−3a$
Answer$−3a (2a^2 − 5a − 4)$
$= −3a \times 2a^2− 5a \times −3a − 4 \times −3a$
$= −6a^3 + 15a^2 + 12a$
View full question & answer→Question 262 Marks
Multiply: $−8x$ and $4 − 2x − x^2$
Answer$−8x (4 − 2x − x^2)$
$= −8x \times 4 −8x \times −2x −8x \times −x^2$
$= −32x + 16x^2 + 8x^3$
View full question & answer→Question 272 Marks
Multiply: $4a$ and $6a + 7$
Answer$4a (6a + 7)$
$= 4a \times 6a + 4a \times 7$
$= 24a^2 + 28a$
View full question & answer→Question 282 Marks
Multiply: $−5cd^2 by − 5cd^2$
Answer$−5cd^2 \times −5cd^2 $
$= (−5 \times −5) (cd^2\times cd^2)$
$= 25c^{1+1}. d^{2+2}$
$= 25c^2d^4$
View full question & answer→Question 292 Marks
Multiply: $\frac{2}{3} \mathrm{ab}$ by $-\frac{1}{4} \mathrm{a}^2 \mathrm{~b}$
Answer$ \frac{2}{3} a b \times-\frac{1}{4} a^2 b$
$=\left(\frac{2}{3} \times \frac{-1}{4}\right)\left(a b \times a^2 b\right)$
$ =-\frac{1}{6} a^{1+2} \cdot b^{1+1}$
$ =-\frac{1}{6} a^3 b^2$
View full question & answer→Question 302 Marks
Multiply : $8ab^2 by − 4a^3b^4$
Answer$8ab^2 \times − 4a^3b^4 = (8 \times − 4)(ab^2 \times a^3b^4)$
$= − 32a^{1+3} . b^{2+4}$
$= − 32a^4b^6$
View full question & answer→Question 312 Marks
How much less $2a^2 + 1$ is than $3a^2 – 6 ?$
Answer$3a^2 – 6$
$+ 2a^2 + 1$
$– –$
$a^2 – 7$
View full question & answer→Question 322 Marks
How much more than $2x^2 + 4xy + 2y^2$ is $5x^2 + 10xy – y^2 ?$
Answer$5x^2 + 10xy – y^2$
$+2x^2 + 4xy + 2y^2$
$– – –$
$3x^2 + 6xy – 3y^2$
View full question & answer→Question 332 Marks
What must be added to $x^4-x^3+x^2+x+3$ to obtain $x^4+x^2-1$ ?
Answer$x^4 + x^2 – 1$
$+x^4 – x^3 + x^2 + x + 3$
$– + – – –$
$x^3 – x – 4$
View full question & answer→Question 342 Marks
Take away $– 3x^3 + 4x^2 – 5x+ 6$ from $3x^3 – 4x^2 + 5x – 6$
Answer$3x^3 – 4x^2 + 5x – 6$
$– 3x^3 + 4x^2 – 5x + 6$
$+ – + –$
$6x^3 – 8x^2 +10x – 12$
View full question & answer→Question 352 Marks
Subtract : $a^2+ ab + b^2$ from $4a^2 − 3ab + 2b^2$
Answer$4a^2 − 3ab + 2b^2$
$+ a^2 + ab + b^2$
$− − −$
$3a^2 − 4ab + b^2$
View full question & answer→Question 362 Marks
Subtract : $cab − 4cad − cbd$ from $3abc + 5bcd − cda$
Answer$3abc + 5bcd − cda$
$+cab − cbd − 4cad$
$− + + $
$2abc + 6bcd + 3cad$
View full question & answer→Question 372 Marks
Subtract : $6a + 3$ from $a^3 − 3a^2 + 4a + 1$
Answer$a^3 − 3a^2 + 4a + 1$
$+ 6a + 3$
$− −$
$a^3 − 3a^2 − 2a − 2$
View full question & answer→Question 382 Marks
Subtract : $x^3 − 4x − 1$ from $3x^3 − x^2 + 6$
Answer$3x^3− x^2 + 6$
$x^3 − 4x − 1$
$− +$
$2x^3 − x^2 + 4x + 7$
View full question & answer→Question 392 Marks
Subtract : $3a − 5b + c + 2d$ from $7a − 3b + c − 2d$
Answer$7a − 3b + c − 2d$
$3a − 5b + c + 2d$
$− + − − $
$4a + 2b − 4d$
View full question & answer→Question 402 Marks
Subtract : $−2x^2y + 3xy^2$ from $8x^2y$
Answer$8x^2y$
$−2x^2y + 3xy^2$
$+ −$
$10x^2y − 3xy^2$
View full question & answer→Question 412 Marks
Find the total savings of a boy who saves $₹ (4x – 6y), ₹ (6x + 2y), ₹ (4y – x)$ and $₹ (y – 2x) $ for four consecutive weeks.
Answer$4x − 6y$
$6x + 2y$
$–x + 4y$
$–2x + y$
$7x + y$
$\therefore$ Total saving $= ₹(7x + y)$
View full question & answer→Question 422 Marks
Add : $x^3 − x^2y + 5xy^2 + y^3, x^3 − 9xy^2 + y^3, 3x^2y + 9xy^2$
Answer$x^3 − x^2y + 5xy^2 + y^3$
$−x^3 − 9xy^2 + y^3$
$+ 3x^2y + 9xy^2$
$2x^2y + 5xy^2 + 2y^3$
View full question & answer→Question 432 Marks
Add : $13ab − 9cd − xy, 5xy, 15cd − 7ab, 6xy − 3cd$
Answer$13ab − 9cd + xy$
$+ 5xy$
$−7ab + 15cd$
$− 3cd + 6xy$
$6ab + 3cd +10xy$
View full question & answer→Question 442 Marks
Add : $a − 3b + 3; 2a + 5 − 3c; 6c − 15 + 6b$
Answer$a − 3b + 3$
$2a − 3c + 5$
$+ 6b + 6c − 15$
$3a + 3b + 3c − 7$
View full question & answer→Question 452 Marks
Add : $3b − 7c + 10, 5c − 2b − 15, 15 + 12c + b$
Answer$3b − 7c + 10$
$−2b + 5c − 15$
$+b + 12c + 15$
$2b + 10c + 10$
View full question & answer→Question 462 Marks
Add : $8x − 3y + 7z, −4x + 5y − 4z, −x − y − 2z$
Answer$8x − 3y + 7z$
$−4x + 5y − 4z$
$−x − y − 2z$
$3x + y + z$
View full question & answer→Question 472 Marks
Add : $5a + 3b, a − 2b, 3a + 5b$
Answer$5a + 3b$
$a − 2b$
$3a + 5b$
$9a + 6b$
View full question & answer→Question 482 Marks
How much bigger is $5x^2y^2 – 18xy^2 – 10x^2y$ than $–5x^2 + 6x^2y – 7xy?$
AnswerThe required result,
$(5x^2y^2 – 18xy^2 – 10x^2y) – (–5x^2 + 6x^2y – 7xy)$
$= 5x^2y^2 – 18xy^2 – 10x^2y + 5x^2 + 6x^2y – 7xy$
$= 5x^2y^2 – 18xy^2 – 16x^2y + 5x^2 + 7xy$
View full question & answer→Question 492 Marks
Evaluate : $3x^2 + 5xy − 4y^2 + x^2 − 8xy − 5y^2$
Answer$3x^2 + 5xy − 4y^2 + x^2 − 8xy − 5y^2$
$= 3x^2 + x^2+ 5xy - 8xy − 4y^2 − 5y^2$
$= 4x^2 − 3xy − 9y^2$
View full question & answer→Question 502 Marks
How much smaller is $15x – 18y + 19z$ than $ 22x – 20y – 13z + 26$ ?
AnswerThe required result is
$(22x – 20y – 13z + 26) – (15x – 18y + 19z)$
$= 22x – 20y – 13z + 26 – 15x + 18y – 19z$
$= 7x – 2y – 32z + 26$
View full question & answer→