Question

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

Answer 1

HERE IS YOUR ANSWER...⬇⬇
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$We \: \: know \: \: that ,\: \\ \\ \boxed{ (x + y) {}^{3} = x {}^{3} + y {}^{3} + 3x {}^{2} y + 3xy {}^{2} }\\ \\ \\ By \: using \: this \: \: formula, \:$

$8x {}^{3} + 27y {}^{3} + 36x {}^{2} y + 54xy {}^{2} \\ \\ = (2x) {}^{3} +( 3y) {}^{3} + 3 \times 4x \times 3y + 3 \times 2x \times 9y \\ \\ =( 2x) {}^{3} + (3y) {}^{3} + 3 \times (2x) {}^{2} \times 3y + 3 \times 2x \times (3y) {}^{2} \\ \\ = (2x + 3y) {}^{3} \\ \\ = (2x + 3y)(2x + 3y)(2x + 3y)$

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✝✝...HOPE IT HELPS YOU...✝✝

Answer 2

HERE IS YOUR ANSWER...⬇⬇
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\begin{lgathered}We \: \: know \: \: that ,\: \\ \\ \boxed{ (x + y) {}^{3} = x {}^{3} + y {}^{3} + 3x {}^{2} y + 3xy {}^{2} }\\ \\ \\ By \: using \: this \: \: formula, \:\end{lgathered}Weknowthat,(x+y)3=x3+y3+3x2y+3xy2​Byusingthisformula,​ 

\begin{lgathered}8x {}^{3} + 27y {}^{3} + 36x {}^{2} y + 54xy {}^{2} \\ \\ = (2x) {}^{3} +( 3y) {}^{3} + 3 \times 4x \times 3y + 3 \times 2x \times 9y \\ \\ =( 2x) {}^{3} + (3y) {}^{3} + 3 \times (2x) {}^{2} \times 3y + 3 \times 2x \times (3y) {}^{2} \\ \\ = (2x + 3y) {}^{3} \\ \\ = (2x + 3y)(2x + 3y)(2x + 3y)\end{lgathered}8x3+27y3+36x2y+54xy2=(2x)3+(3y)3+3×4x×3y+3×2x×9y=(2x)3+(3y)3+3×(2x)2×3y+3×2x×(3y)2=(2x+3y)3=(2x+3y)(2x+3y)(2x+3y)​