Question

Factorize using Algebraic Identities.

1- 25x² + 100x + 100
2- 36x² - 169y²

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

1- (5x+10)(5x+10)

2- (6x+13y)(6x-13y)

Step-by-step explanation:

1-

$25x {}^{2} + 100x + 100 \\ =(5x) {}^{2} + 2 \times 5 \times 10 + (10x) {}^{2} \\ since \: \: \: x {}^{2} + 2xy + {y}^{2} = (x + y) {}^{2} \\ therefore \: \: \: (5x) {}^{2} + 2 \times 5 \times 10 + (10x) {}^{2} = (5x + 10) {}^{2} \\ = (5x + 10)(5x + 10)$

2-

$36x {}^{2} - 169y {}^{2} \\ = (6x){}^{2} - (13y) {}^{2} \\ = since (x {}^{2} - y {}^{2}) = (x + y)(x - y) \\ therefore(6x){}^{2} - (13y) {}^{2} = (6x + 13y)(6x - 13y)$

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