Factorize: 8x^3 + y^3 + 12x^2y + 6xy^2 - Vidyadip

Question

Factorize: $8x^3 + y^3 + 12x^2y + 6xy^2$

✓

Answer

$8x^3 + y^3 + 12x^2y + 6xy^2$
$= (2x)^3 + y^3 + 3 \times (2x)^2 \times y + 3(2\times ) \times y^2$
$= (2x + y)^3 \big[\because a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^3\big]$
$= (2x + y)(2x + y)(2x + y)$
$\therefore 8x^3 + y^3 + 12x^2y + 6xy^2$
$= (2x + y)(2x + y)(2x + y)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Factorization Of Algebraic Expressions→Factorization Of Algebraic Expressions — all question types→MATHS STD 9 question papers→Rajasthan Board STD 9 question papers→Rajasthan Board question paper generator→

Similar questions

Find the following products:
$\Big(\frac{3}{\text{x}}-\frac{5}{\text{y}}\Big)\Big(\frac{9}{\text{x}^2}+\frac{25}{\text{y}^2}+\frac{15}{\text{xy}}\Big)$

Factorise : $6x^2 - 11x - 35$

Rationalise the denominator of the following:
$\frac{3-2\sqrt{2}}{3+2\sqrt{2}}$

Check the following are solutions of the equation 2x - y = 6 and which are not:
(0, 6)

Factorise:$a^2 + ab(b + 1) + b^3$

By Remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where:$ p(x) = 4x^3 - 12x^2 + 14x - 3, g(x) = 2x - 1$

Retionalise the denominator of each of the following:
$\frac{\sqrt3+1}{2}$

In the following two polynomials, find the value of a, if $x + a$ is a factor. $x^3 + ax^2 - 2x + a + 4$

Two supplementary angles are in the ratio 4 : 5. Find the angles.

Factorize the following expressions: $y^3 + 125$