State whether the statement is True or False.
The cube of $(2 a + 3 b)$ is equal to $8 a^{3} + 36 a^{2} b + 54 a b^{2} + 27 b^{3}$ .

True

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False

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Solution

The correct option is A True
${(a + b)}^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2} (2 a + 3 b)^{3} = 27 b^{3} + 8 a^{3} + 54 b^{2} a + 36 b a^{2}$

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(3 b - 2 a)

27 b^{3} - 54 b^{2} a + 36 b a^{2} - 8 a^{3}

(2 a - 3 b)^{3}

= 8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2}

(2 a - 1)

8 a^{3} - 12 a^{2} + 6 a - 1

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