How do you multiply ${(x + 5 y)}^{3}$ $(x + 5y)^3$ ?

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Answer 1 · 2018-06-29T00:36:13

$x^{3} + 15 x^{2} y + 75 x y^{2} + 125 y^{3}$ $x^3+15x^2y+75xy^2+125y^3$

Given: ${(x + 5 y)}^{3}$ $(x+5y)^3$ .

Use the fact that ${(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ $(a+b)^3=a^3+3a^2b+3ab^2+b^3$ .

Letting $a = x, b = 5 y$ $a=x,b=5y$ , we get:

$= x^{3} + 3 \cdot x^{2} \cdot 5 y + 3 \cdot x \cdot {(5 y)}^{2} + {(5 y)}^{3}$ $=x^3+3*x^2*5y+3*x*(5y)^2+(5y)^3$

$= x^{3} + 15 x^{2} y + 3 x \cdot 25 y^{2} + 125 y^{3}$ $=x^3+15x^2y+3x*25y^2+125y^3$

$= x^{3} + 15 x^{2} y + 75 x y^{2} + 125 y^{3}$ $=x^3+15x^2y+75xy^2+125y^3$

How do you multiply (x + 5y)^3(x+5y)3(x + 5y)^3?