Question

Expand the expression to a polynomial in standard form:
left parenthesis, x, plus, 3, right parenthesis, left parenthesis, 4, x, minus, 1, right parenthesis, left parenthesis, x, minus, 1, right parenthesis
(x+3)(4x−1)(x−1)







Solve the problem just like the example below
⬇️
Expand the expression to a polynomial in standard form:
left parenthesis, 2, x, plus, 1, right parenthesis, left parenthesis, 3, x, minus, 5, right parenthesis, left parenthesis, 3, x, plus, 1, right parenthesis
(2x+1)(3x−5)(3x+1)
left parenthesis, 2, x, plus, 1, right parenthesis, left parenthesis, 9, x, squared, minus, 12, x, minus, 5, right parenthesis
(2x+1)(9x
2
−12x−5)

9, x, squared
9x
2
minus, 12, x
−12x
minus, 5
−5
2, x
2x
18, x, cubed
18x
3
minus, 24, x, squared
−24x
2
minus, 10, x
−10x
plus, 1
+1
9, x, squared
9x
2
minus, 12, x
−12x
minus, 5
−5
Combine like terms:
Combine like terms:
18, x, cubed, minus, 15, x, squared, minus, 22, x, minus, 5
18x
3
−15x
2
−22x−5

Answer 1

Let's expand the expression \((x + 3)(4x - 1)(x - 1)\) step by step, following the format of your example.

1. **Expand the first two binomials**:
\[
(x + 3)(4x - 1)
\]
Apply the distributive property (FOIL):
\[
= x(4x) + x(-1) + 3(4x) + 3(-1)
\]
\[
= 4x^2 - x + 12x - 3
\]
Combine like terms:
\[
= 4x^2 + 11x - 3
\]

2. **Now, multiply by the third binomial**:
\[
(4x^2 + 11x - 3)(x - 1)
\]
Apply the distributive property:
\[
= 4x^2(x) + 4x^2(-1) + 11x(x) + 11x(-1) - 3(x) + (-3)(-1)
\]
\[
= 4x^3 - 4x^2 + 11x^2 - 11x - 3x + 3
\]

3. **Combine the terms**:
\[
= 4x^3 + (-4x^2 + 11x^2) + (-11x - 3x) + 3
\]
\[
= 4x^3 + 7x^2 - 14x + 3
\]

4. **Write in standard form**:
The final expression in standard form is:
\[
\boxed{4x^3 + 7x^2 - 14x + 3}
\]