Question

25 (a+b)^2 - 16 (a-b)^2
Find answer by using factorisation​

Answer 1

Answer: 25(a+b)^2 - 16(a-b)^2

=> [ 5(a+b)]^2 - [ 4(a-b)]^2

=> (5a +5b)^2 - (4a-4b)^2

=> (5a +5b - 4a +4b) ( 5a +5b +4a - 4b)

=> (a +9b) (9a+b)

Answer 2

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: 25 {(a + b)}^{2} - 16 {(a - b)}^{2}$

can be rewritten as

$\rm \: = 5 \times 5 \times {(a + b)}^{2} - 4 \times 4 \times {(a - b)}^{2}$

$\rm \: = \: {(5[a + b])}^{2} - {(4[a - b])}^{2}$

$\rm \: = \: {(5a + 5b)}^{2} - {(4a - 4b)}^{2}$

We know,

$\boxed{ \rm{ \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }}$

Now, here

$\rm \: x = 5a + 5b$

and

$\rm \: y = 4a - 4b$

So, on substituting the values, we get

$\rm \: = \: (5a + 5b + 4a - 4b)(5a + 5b - 4a + 4b)$

$\rm \: = \: (9a + b)(a + 9b)$

Hence,

$\rm\implies \:25 {(a + b)}^{2} - 16 {(a - b)}^{2}=(9a + b)(a + 9b)$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$