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Question
Expand : (2a + b)3
Sum
Solution 1
(2a + b)3 = (2a)3 + (b)3 + 3×2a×b(2a + b) ...[(a + b)3 = a3 + b3 + 3ab(a + b)]
= 8a3 + b3 + 6ab (2a + b)
= 8a3 + b3 + 12a2b + 6ab2
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Solution 2
To expand (2a+b)3, we use the binomial expansion formula:
(x+y)3 = x3 + 3x2y + 3xy2 + y3
Here, x = 2a and y = b.
Apply the formula
(2a + b)3 = (2a)3 + 3(2a)2(b) + 3(2a)(b)2 + (b)3
Simplify each term
- (2a)3 = 8a3
- 3(2a)2(b) = 3(4a2)(b) = 12a2b
- 3(2a)(b)2 = 3(2a)(b2) = 6ab2
- (b)3 = b3
Combine the terms
(2a+b)3 = 8a3 + 12a2b + 6ab2 + b3
8a3 + 12a2b + 6ab2 + b3
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Cubes of Binomials
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