Factorize $25 x^{2} + 60 x + 36$ $25x^2+60x+36$ ?

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Factorize $25 x^{2} + 60 x + 36$ $25x^2+60x+36$ ?

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Answer 1 · 2016-07-26T03:58:34

$25 x^{2} + 60 x + 36 = {(5 x + 6)}^{2}$ $25x^2+60x+36=(5x+6)^2$

Explanation:

In $25 x^{2} + 60 x + 36$ $25x^2+60x+36$ , the first and third term are complete square as $25 x^{2} = {(5 x)}^{2}$ $25x^2=(5x)^2$ and $36 = 6^{2}$ $36=6^2$ and middle term is double the product of $5 x$ $5x$ and $3$ $3$ i.e. $2 \times 5 x \times 6 = 60 x$ $2xx5x xx6=60x$

Hence using the identity ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $(a+b)^2=a^2+2ab+b^2$

$25 x^{2} + 60 x + 36$ $25x^2+60x+36$

= ${(5 x)}^{2} + 2 \times 5 x \times 6 x + 6^{2}$ $(5x)^2+2xx5x xx6x+6^2$

= ${(5 x + 6)}^{2}$ $(5x+6)^2$

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Factorize $25 x^{2} + 60 x + 36$ $25x^2+60x+36$ ?

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