Questions · Page 2 of 2

[3 marks sum]

Question 513 Marks
factorise: $3a^2 - 5a + 2$
Answer
$3a^2 - 5a + 2$
$= 3a2 - 3a - 2a + 2$
$= 3a (a - 1) - 2(a - 1)$
$= (a - 1)(3a - 2)$
 
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Question 523 Marks
Factorise: $1 - 25 (a+ b)^2$
Answer
$1 - 25 (a+ b)^2$
$= (1)^2 - [5(a+b)]^2$
$= [1 + 5(a+b)] [1 - 5(a+b)]$
$= (1 + 5a + 5b) (1 - 5a - 5b)$
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Question 533 Marks
Factorise: $a^4 - (a^2 - 3b^2)^2$
Answer
$a^4 - (a^2 - 3b^2)^2$
$= (a^2)^2 - (a^2 - 3b^2)^2$
$= (a^2 + a^2 - 3b^2) (a^2 - a^2 + 3b^2)$
$= (2a^2 - 3b^2) (3b)^2$
$= 3b^2 (2a^2 - 3b^2)$
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Question 543 Marks
Factorise: $(5a - 3b)^2 - 16b^2$
Answer
$(5a - 3b)^2 - 16b^2$
$= (5a - 3b)^2 - (4b)^2$
$= (5a - 3b + 4b) (5a - 3b - 4b)$
$= (5a + b) (5a - 7b)$
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Question 553 Marks
Factorise: $(a+ 2b)^2 - a^2$
Answer
$(a+ 2b)^2 - a^2$
$= (a+ 2b)^2 - (a)^2$
$= (a + 2b + a) (a + 2b - a)$
$= (2a + 2b) (2b)$
$= 2 (a + b) (2b)$
$= 2 \times 2b (a + b)$
$= 4b (a + b)$
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Question 563 Marks
factorise: $x^2 + 6x + 9 - 4y^2$
Answer
$x^2 + 6x + 9 - 4y^2$
$= (x)^2 + 2 \times x \times 3 + (3)^2 - (2y)^2$
$...[(a + b)^2 = a^2 + 2ab + b^2]$
$...[a^2 - b^2 = (a + b)(a - b)]$
$= (x + 3)^2 - (2y)^2$
$= (x + 3 + 2y) (x + 3 - 2y)$
$= (x + 2y + 3) (x - 2y + 3)$
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Question 573 Marks
Factorise: $a^2 - b^2 - 2b - 1$
Answer
$a^2 - b^2 - 2b - 1$
$= a^2 - (b^2 + 2b + 1)$
$...[(a + b)^2 = a^2 + b^2 + 2ab]$
$...[a^2 - b^2 = (a + b) (a - b)]$
$= (a)^2 - (b + 1)^2$
$= (a + b + 1)(a - b - 1)$
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Question 583 Marks
Factorise: $a^2 + 4a + 4 - b^2$
Answer
$a^2 + 4a + 4 - b^2....[(a + b)^2 = a^2 + 2ab + b^2]$
$....[a^2 - b^2 = (a + b)(a - b)]$
$= (a)^2 + 2 \times a \times 2 + (2)^2 - (b)^2$
$= (a + 2)^2 - (b)^2$
$= (a + 2 + b) (a + 2 - b)$
$= (a + b + 2) (a - b + 2)$
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Question 593 Marks
Factorise: $\left(7 \frac{3}{10}\right)^2-\left(2 \frac{1}{10}\right)^2$
Answer
$ \left(7 \frac{3}{10}\right)^2-\left(2 \frac{1}{10}\right)^2$
$ =\left(\frac{73}{10}\right)^2-\left(\frac{21}{10}\right)^2$
$ =\left(\frac{73}{10}+\frac{21}{10}\right)\left(\frac{73}{10}-\frac{21}{10}\right) \ldots\left[\mathrm{a}^2-\mathrm{b}^2=(\mathrm{a}+\mathrm{b})(\mathrm{a}-\mathrm{b})\right]$
$ =\left(\frac{94}{10}\right)\left(\frac{52}{10}\right)$
$ =\left(\frac{47}{5}\right)\left(\frac{26}{5}\right)=\frac{1222}{25}=48 \frac{22}{25}$
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Question 603 Marks
Factorise: $\left(6 \frac{2}{3}\right)^2-\left(2 \frac{1}{3}\right)^2$
Answer
$ \left(6 \frac{2}{3}\right)^2-\left(2 \frac{1}{3}\right)^2$
$ =\left(\frac{20}{3}\right)^2-\left(\frac{7}{3}\right)^2$
$ =\left(\frac{20}{3}+\frac{7}{3}\right)\left(\frac{20}{3}-\frac{7}{3}\right)$
$ =\left(\frac{27}{3}\right)\left(\frac{13}{3}\right)=9 \times \frac{13}{3}=39$
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Question 613 Marks
Factorise : $6a^2 - 3a^2b - bc^2 + 2c^2$
Answer
$6a^2 - 3a^2b - bc^2 + 2c^{2}$
$= 6a^2 - 3a^2b + 2c^2 - bc^2$
$= 3a^2 (2 - b) + c^2 (2 - b)$
$= (2 - b) (3a^2 + c^2)$
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Question 623 Marks
Factorise : $- x^2y - x + 3xy + 3$
Answer
$- x^2y - x + 3xy + 3$
$= 3 - x + 3xy - x^2y$
$= 1(3 - x) + xy (3 - x)$
$= (3 - x) (1 + xy)$
$= (xy + 1) (3 - x)$
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Question 633 Marks
Factorise : $ab(c^2 + d^2) - a^2cd - b^2cd$
Answer
$ab(c^2 + d^2) - a^2cd - b^2cd$
$= abc^2 + abd^2 - a^2cd - b^2cd$
$= abc^2 - a^2cd - b^2cd + abd^2$
$= ac (bc - ad) - bd (bc - ad)$
$= (bc - ad) (ac - bd)$
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Question 643 Marks
Factorise : $a^3 - a^2 - ab + a + b - 1$
Answer
$a^3 - a^2 - ab + a + b - 1$
$= a^3 - a^2 - ab + b + a - 1$
$= a^2 (a - 1) - b (a - 1) + 1 (a - 1)$
$= (a - 1) (a^2 - b + 1)$
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Question 653 Marks
Factorise : $(a^2 - b^2) c + (b^2 - c^2)a$
Answer
$(a^2 - b^2) c + (b^2 - c^2)a$
$= a^2c - b^2c + ab2 - ac^2$
$= a^2c - ac^2 + ab^2 - b^2c$
$= ac (a - c) + b^2 (a - c)$
$= (a - c) (ac + b^2)$
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Question 663 Marks
Factorise : $x^2 - (b - 2)x - 2b$
Answer
$x^2 - (b - 2)x - 2b$
$= x^2 - bx + 2x - 2b$
$= x (x - b) + 2(x - b)$
$= (x - b) (x + 2)$
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Question 673 Marks
Factorise : $x^2 - (a - 3)x - 3a$
Answer
$x^2 - (a - 3)x - 3a$
$= x^2 - ax + 3x - 3a$
$= x (x - a) + 3 (x - a)$
$= (x - a) (x + 3)$
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Question 683 Marks
Factorise : $3a^2b - 12a^2 - 9b + 36$
Answer
$3a^2b - 12a^2 - 9b + 36$
$= 3a^2 (b - 4) - 9 (b - 4)$
$= (b - 4) (3a^2- 9)$
$= (b - 4) 3 (a^2 - 3)$
$= 3 (b - 4) (a^2-3)$
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[3 marks sum] - Page 2 - MATHS STD 8 Questions - Vidyadip