Question

$14(3y + 5z) ^{3} + 7(3y - 5z) ^{2}$

Answer 1

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$<i>$
Given :



$\tt{14(3y + 5z)^3 + 7(3y - 5z)^2}$



${\boxed{\tt{(a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2}}}$


${\boxed{\tt{(a - b)^2 = a^2 - 2ab + b^2}}}$



${\tt{\underline{Here, \ a = 3y, \ b = 5z}}}$




$\tt{\Rightarrow 14[(3y)^3 + (5z)^3 + (3)(3y)^2(5z) +}$
$\tt{(3)(3y)(5z)^2] + 7[(3y)^2 - (2)(3y)(5z) +}$
$\tt{(5z)^2]}$




$\tt{\Rightarrow 14[27y^3 + 125z^3 + 135y^2z + 225yz^2]}$
$\tt{+ 7[9y^2 - 30yz + 25y^2]}$




${\tt{\underline{Taking \ 7 \ as \ common.}}}$




$\tt{\Rightarrow 7 \{ 2[27y^3 + 125z^3 + 135y^2z +}$
$\tt{225yz^2] + 1[9y^2 - 30yz + 25y^2] \}}$





$\tt{\Rightarrow 7\{ 54y^3 + 250z^3 + 270y^2z + 450yz^2}$
$\tt{+ 9y^2 - 30yz + 25y^2 \}}$




$\tt\red{\Rightarrow 378y^3 + 1750z^3 + 1890y^2z +}$
$\tt\red{3150yz^2 + 63y^2 - 210yz + 175y^2}$





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