Write the form in expanded form $(2 a + 3 b)^{3}$

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Solution

We have,

${(2 a + 3 b)}^{3}$

Since,

${(x + y)}^{3} = x^{3} + y^{3} + 3 x y (x + y)$

Therefore,

${(2 a + 3 b)}^{3} = {(2 a)}^{3} + {(3 b)}^{3} + 3 \times 2 a \times 3 b (2 a + 3 b)$

${(2 a + 3 b)}^{3} = 8 a^{3} + 27^{3} + 18 a b (2 a + 3 b)$

${(2 a + 3 b)}^{3} = 8 a^{3} + 27^{3} + 36 a^{2} b + 54 a b^{2}$

Hence, this is the answer.

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