The correct option is A 27a^3 + 135a^2 b + 225 ab^2 + 125b^3 We know, #160; (A+B)^3=A^3+B^3+3A^2B+3AB^2 Then, (3a+5b)^3 =(3a)^3+(5b)^3+3(3a ...

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Algebraic Identities

Expand 3a +...

Question

Expand $(3 a + 5 b)^{3}$ .

27 a^{3} + 135 a^{2} b + 225 a b^{2} + 125 b^{3}

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27 a^{3} - 135 a^{2} b + 225 a b^{2} + 125 b^{3}

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27 a^{3} + 135 a^{2} b - 225 a b^{2} + 125 b^{3}

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None of these

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Solution

The correct option is A $27 a^{3} + 135 a^{2} b + 225 a b^{2} + 125 b^{3}$
We know, $(A + B)^{3} = A^{3} + B^{3} + 3 A^{2} B + 3 A B^{2}$

Then,
$(3 a + 5 b)^{3}$
$= (3 a)^{3} + (5 b)^{3} + 3 (3 a)^{2} 5 b + 3 (5 b)^{2} 3 a$
$= 27 a^{3} + 125 b^{3} + 3 (9 a^{2}) (5 b) + 3 (3 a) (25 b^{2})$
$= 27 a^{3} + 125 b^{3} + 135 a^{2} b + 225 a b^{2}$ .

Therefore, option $A$ is correct.

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Similar questions

If $3 a + 5 b + 4 c = 0$ , show that:
$27 a^{3} + 125 b^{3} + 64 c^{3} = 180 a b c$ .

3 a + 5 b + 4 c = 0

27 a^{3} + 125 b^{3} + 64 c^{3} = 180 a b c

If 3a + 5b + 4c = 0, Find the value of $27 a^{3} + 125 b^{3} + 64 c^{3}$ .

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