Question

factorise 4a(a-b)^2-25(a+b)^2​

Answer 1

Step-by-step explanation:

49(a−b)

2

−25(a+b)

2

=7

2

(a−b)

2

−5

2

(a+b)

2

=[7(a−b)]

2

−[5(a+b)]

2

=(7a−7b)

2

−(5a+5b)

2

=[(7a−7b)+(5a+5b)][(7a−7b)−(5a+5b)]

\blue {( By \: Algebraic \:Identity )}(ByAlgebraicIdentity)

\boxed { \pink { x^{2} - y^{2} = ( x + y )( x - y ) }}

x

2

−y

2

=(x+y)(x−y)

\begin{gathered} = [7a-7b+5a+5b][7a-7b-5a-5b] \\= ( 7a+5a-7b+5b)(7a-5a-7b-5b)\\= (12a-2b)(2a-12b)\\= [2(6a-b)][ 2(a-6b)] \\= 4(6a-b)(a-6b) \end{gathered}

=[7a−7b+5a+5b][7a−7b−5a−5b]

=(7a+5a−7b+5b)(7a−5a−7b−5b)

=(12a−2b)(2a−12b)

=[2(6a−b)][2(a−6b)]

=4(6a−b)(a−6b)

Therefore.,

\begin{gathered} \red{ Factors \:of \:49(a-b)^{2} - 25(a+b)^{2}}\\\green {= 4(6a-b)(a-6b)} \end{gathered}

Factorsof49(a−b)

2

−25(a+b)

2

=4(6a−b)(a−6b)

Answer 2

Step-by-step explanation:

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