What is factor (x+y)^3+512(m-n)^3 ?

The solution to factor (x+y)^3+512(m-n)^3 is (x+y+8(m-n))((x+y)^2-8(x+y)(m-n)+64(m-n)^2)

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factor (x+y)^3+512(m-n)^3

factor

(x + y)^{3} + 512 (m - n)^{3}

(x + y + 8 (m - n)) ((x + y)^{2} - 8 (x + y) (m - n) + 64 (m - n)^{2})

Solution steps

(x + y)^{3} + 512 (m - n)^{3}

Rewrite

(x + y)^{3} + 512 (m - n)^{3}

(x + y)^{3} + (8 (m - n))^{3}

= (x + y)^{3} + (8 (m - n))^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(x + y)^{3} + (8 (m - n))^{3} = ((x + y) + 8 (m - n)) ((x + y)^{2} - 8 (x + y) (m - n) + 8^{2} (m - n)^{2})

= ((x + y) + 8 (m - n)) ((x + y)^{2} - 8 (x + y) (m - n) + 8^{2} (m - n)^{2})

Refine

= (x + y + 8 (m - n)) (64 (m - n)^{2} - 8 (x + y) (m - n) + (x + y)^{2})

2 0^{2} + x^{2}

5.8 x^{10} - 3 x^{2.17}

\frac{d}{d u} ((x (u)) (u)^{3})

2 x y - z - 2 x z + y

[m^{2} - 7] + n^{2}

What is factor (x+y)^3+512(m-n)^3 ?
The solution to factor (x+y)^3+512(m-n)^3 is (x+y+8(m-n))((x+y)^2-8(x+y)(m-n)+64(m-n)^2)