Question

$(9x + y)(9x + y)$
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Answer 1

$\mathfrak{\pmb{{\underline{To~solve}}:}}$

• (9x + y)(9x + y)

$\mathfrak{\pmb{{\underline{Solution}}:}}$

$\sf{{\pmb{{\underline{Identity}}:}}(a+b)(a+b)=a^{2}+2ab+b^{2}}$

$\sf \implies (9x + y)(9x + y) = (9x)^{2} + 2(9x)(y) + {(y)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf = 81 {x}^{2} + 2(9xy) + {y}^{2} \\ \sf = \blue{ \underline{ \boxed{ \sf{ \pmb{ {81x}^{2} + 18xy + {y}^{2} }}}}}$

$\mathfrak{ \therefore{\pmb{{\underline{Required~answer}}:}}}$

• $\sf (9x + y)(9x + y) = \blue{ \underline{ \underline{ \sf{ \pmb{ {81x}^{2} + 18xy + {y}^{2} }}}}}$

$\mathfrak{\pmb{{\underline{More~information}}:}}$

$\sf{{\pmb{{\underline{Identities}}:}}}$

• $\sf{(a+b)(a+b)={\underline{\underline{\pmb{a^{2}+2ab+b^{2}}}}}}$

• $\sf{(a-b)(a-b)={\underline{\underline{\pmb{a^{2}-2ab+b^{2}}}}}}$

• $\sf{(a+b)(a-b)={\underline{\underline{\pmb{a^{2}-b^{2}}}}}}$

• $\sf{(x+a)(x+b)={\underline{\underline{\pmb{x^{2}+(a+b)x+ab}}}}}$

Answer 2

Question:

• (9x + y)(9x + y)

Solution:

As we know that,

• (a + b)² = a² + 2ab + b²

Given:

• a = 9x
• b = y

Putting the values on formula,

➨(9x + y)² = (9x)² + 2(9x)(y) + (y)²

➨(9x + y)² = 81x² + 18xy + y²

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