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We are asked to expand the expression $(4a - 3b)^2$.

AlgebraAlgebraic ExpansionBinomial TheoremPolynomials
2025/4/27

1. Problem Description

We are asked to expand the expression (4a−3b)2(4a - 3b)^2.

2. Solution Steps

We can expand the expression using the formula (x−y)2=x2−2xy+y2(x-y)^2 = x^2 - 2xy + y^2.
Here, x=4ax = 4a and y=3by = 3b.
Therefore,
(4a−3b)2=(4a)2−2(4a)(3b)+(3b)2(4a - 3b)^2 = (4a)^2 - 2(4a)(3b) + (3b)^2
=16a2−24ab+9b2= 16a^2 - 24ab + 9b^2
The formula used is:
(x−y)2=x2−2xy+y2(x - y)^2 = x^2 - 2xy + y^2

3. Final Answer

16a2−24ab+9b216a^2 - 24ab + 9b^2

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