Q. 4 F4.5( 11 Votes )

# Factories the following

4 (a + b)^{2} – 9 (a – b)^{2}

Answer :

In the given expression

We know that

(a + b)^{2} = a^{2} + 2ab + b^{2}

(a-b)^{2} = a^{2}-2ab + b^{2}

Hence

4[a^{2} + 2ab + b^{2}] – 9[a^{2}-2ab + b^{2}]

4a^{2} + 8ab + 4b^{2} - 9a^{2} + 18ab - 9b^{2}

26ab – 5a^{2} - 5b^{2}

25ab + ab – 5a^{2} – 5b^{2}

[25ab – 5a^{2}] + [ab – 5b^{2}]

5a[5b – a] – b[5b – a]

[5a – b][5b – a]

Hence the factors 4 (a + b)^{2} – 9 (a – b)^{2} are [5a – b] and [5b – a]

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