I need this for my homework plz

Question

Tony multipled the polynomial as shown below.

(4x-1)^3=64x^3-16x^2+4x-1

1)Explain the error in detail.

2)Multiply the polynomial correctly entering each step as you go.Simplify completely.

Answer 1

The cubic expansion is:

(a + b)³ = a³ + 3a²b + 3ab² + b³

However, in the given expansion, we're missing the multiplications by 3 in the 2 middle terms. As you can see:

a²b = (16x²)(-1) = -16x²

ab² = (4x)(1) = 4x

So, to get the correct expansion, use the actual formula:

(4x - 1)³ = 64x³ + 3(16x²)(-1) + 3(4x)(1) - 1 = 64x³ - 48x² + 12x - 1