Factorize 8x-3 - 36x-2y - 54xy-2 - 27y-3- - Maths Q-A

Factorize the polynomial:8x^3+36x^2y+54xy^2+27y^30ex0ex=(2x)^3+(3y)^3+3×(2x)^2×(3y)+3× 2x×(3y)^2use the identity a^3+b^3+3a^2b+3ab^2=(a+b)^38x^3+36x^2y+54xy^2+2 ...

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Byju's Answer

Standard X

Mathematics

Multiplication of Rational Expressions

Factorize 8x^...

Question

Factorize $8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}$ .

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Solution

Factorize the polynomial:
$8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} = {(2 x)}^{3} + {(3 y)}^{3} + 3 \times {(2 x)}^{2} \times (3 y) + 3 \times 2 x \times {(3 y)}^{2}$
use the identity $a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2} = {(a + b)}^{3}$
$8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} = {(2 x + 3 y)}^{3}$
Hence the factorized form of polynomial $8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}$ is $(2 x + 3 y) (2 x + 3 y) (2 x + 3 y)$

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Factorize 8x3+36x2y+54xy2+27y3.

Factorize the polynomial:8x3+36x2y+54xy2+27y3=(2x)3+(3y)3+3×(2x)2×(3y)+3×2x×(3y)2use the identity a3+b3+3a2b+3ab2=(a+b)38x3+36x2y+54xy2+27y3=(2x+3y)3Hence the factorized form of polynomial 8x3+36x2y+54xy2+27y3 is 2x+3y2x+3y2x+3y

Factorize $8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}$ .