Factor 20u^2+20uv+5v^2

Math
20u2+20uv+5v2
Factor 5 out of 20u2+20uv+5v2.
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Factor 5 out of 20u2.
5(4u2)+20uv+5v2
Factor 5 out of 20uv.
5(4u2)+5(4uv)+5v2
Factor 5 out of 5v2.
5(4u2)+5(4uv)+5(v2)
Factor 5 out of 5(4u2)+5(4uv).
5(4u2+4uv)+5(v2)
Factor 5 out of 5(4u2+4uv)+5(v2).
5(4u2+4uv+v2)
5(4u2+4uv+v2)
Factor using the perfect square rule.
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Rewrite 4u2 as (2u)2.
5((2u)2+4uv+v2)
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
4uv=2⋅(2u)⋅v
Rewrite the polynomial.
5((2u)2+2⋅(2u)⋅v+v2)
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=2u and b=v.
5(2u+v)2
5(2u+v)2
Factor 20u^2+20uv+5v^2

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