How do you factor $4x^2 -20xy+25y^2$ ?

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How do you factor $4x^2 -20xy+25y^2$ ?

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Answer 1 · 2015-10-15T13:22:44

(2x-5y)(2x-5y).

Explanation:

$4x^2-20xy+25y^2$
$=4x^2-10xy-10xy+25y^2$
$=2x(2x-5y)-5y(2x-5y)$
$=(2x-5y)(2x-5y)$

Answer 2 · 2015-10-15T13:37:01

$4x^2+20xy+25y^2=(2x+5y)^2$

Explanation:

Use the formula for the square of a binomial: $(a+b)^2=a^2+2ab+b^2$ .

Both $4$ and $25$ , the coefficient of $x^2$ and $y^2$ , are perfect squares. This makes us think that the whole expression could be a perfect square: $4$ is $2^2$ , and $25$ is $5^2$ . So, our claim is that

$4x^2-20xy+25y^2$ is $(2x-5y)^2$ . Is it true? The only term to verify is $-20xy$ , and it is indeed twice the product of $2x$ and $-5y$ . So, the conjecture was right.

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How do you factor $4x^2 -20xy+25y^2$ ?

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