How do you factor $36 x^{2} + 96 x y + 64 y^{2}$ $36x^2+96xy+64y^2$ ?

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How do you factor $36 x^{2} + 96 x y + 64 y^{2}$ $36x^2+96xy+64y^2$ ?

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Answer 1 · 2016-08-29T14:51:34

$4 {(3 x + 4 y)}^{2}$ $4(3x+4y)^2$

Explanation:

$36 x^{2} + 96 x y + 64 y^{2} = 4 (9 x^{2} + 24 x y + 16 y^{2}) = 4 {(3 x + 4 y)}^{2}$ $36x^2+96xy+64y^2 = 4(9x^2+24 x y + 16 y^2) = 4(3x+4y)^2$

Answer 2 · 2016-08-29T14:54:48

$36 x^{2} + 96 x y + 64 y^{2} = 4 {(3 x + 4 y)}^{2}$ $36x^2+96xy+64y^2=4(3x+4y)^2$

Explanation:

Note that all of the coefficients are divisible by $4$ $4$ , so we can separate that out as a scalar factor. Then noticing that the first and last terms are perfect squares, we find that the middle term matches the pattern:

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

with $a = 3 x$ $a=3x$ and $b = 4 y$ $b=4y$ as follows:

$36 x^{2} + 96 x y + 64 y^{2}$ $36x^2+96xy+64y^2$

$= 4 (9 x^{2} + 24 x y + 16 y^{2})$ $=4(9x^2+24xy+16y^2)$

$= 4 ({(3 x)}^{2} + 2 (3 x) (4 y) + {(4 y)}^{2})$ $=4((3x)^2+2(3x)(4y)+(4y)^2)$

$= 4 {(3 x + 4 y)}^{2}$ $=4(3x+4y)^2$

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How do you factor $36 x^{2} + 96 x y + 64 y^{2}$ $36x^2+96xy+64y^2$ ?

2 Answers

Explanation:

Explanation:

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