Question

Factorise 9x square y square-16

Answer 1

SOLUTION

TO FACTORISE

$\sf{9 {x}^{2} {y}^{2} - 16}$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

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

EVALUATION

$\sf{9 {x}^{2} {y}^{2} - 16}$

$\sf{ = {(3xy)}^{2} - {(4)}^{2} }$

$\sf{ = (3xy + 4)(3xy - 4)} \: \: \: \: \: \: (using \: above \: identity \: )$

FINAL ANSWER

$\boxed{ \: \sf{9 {x}^{2} {y}^{2} - 16} = (3xy + 4)(3xy - 4) \: }$

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Answer 2

$\textbf{Given:}$

$\mathsf{9x^2y^2-16}$

$\textbf{To find:}$

$\mathsf{Factors\;of\;9x^2y^2-16}$

$\textbf{Solution:}$

$\boxed{\begin{minipage}{8cm} \textsf{The method of writing a polynomial into product of}\\\\\textsf{its factors is called factorization} \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{9x^2y^2-16}$

$\mathsf{=(3xy)^2-4^2}$

$\mathsf{Using\;identity,\;\bf\,a^2-b^2=(a-b)(a+b)}$

$\mathsf{=(3xy-4)(3xy+4)}$

$\implies\boxed{\mathsf{9x^2y^2-16=(3xy-4)(3xy+4)}}$

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