Expand $(4 x + 5 y)^{3}$ .

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Solution

To expand the expression.
The given expression is $(4 x + 5 y)^{3}$ .
To expand the expression we use the identity $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$ .
Comparing given expression with identity we have, $a = 4 x, b = 5 y$ .
Substituting values in identity we get:
${(4 x + 5 y)}^{3} = {(4 x)}^{3} + {(5 y)}^{3} + 3 (4 x) (5 y) (4 x + 5 y) = 64 x^{3} + 125 y^{3} + 60 x y (4 x + 5 y) = 64 x^{3} + 125 y^{3} + 240 x^{2} y + 300 x y^{2}$

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