Factorise : 49 a^{2}+70 a b+25 b^{2}

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2. Polynomials

easy

Factorise : $49 a^{2}+70 a b+25 b^{2}$

Option A

Option B

Option C

Option D

Solution

Here you can see that

$49 a^{2}=(7 a)^{2}, 25 b^{2}=(5 b)^{2}, 70 a b=2(7 a)(5 b)$

Comparing the given expression with $x^{2}+2 x y+y^{2},$ we observe that $x=7 a$ and $y=5 b$ Using Identity $I$, we get

$49 a^{2}+70 a b+25 b^{2}=(7 a+5 b)^{2}=(7 a+5 b)(7 a+5 b)$

Standard 9

Mathematics

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