### Home > A2C > Chapter 4 > Lesson 4.3.2 > Problem4-155

4-155.

Multiply the expressions in parts (a) through (c) to remove the parentheses. Homework Help ✎

1. $(x − 1)(x + 1)$

Use a generic rectangle to multiply.

In a rectangle, (length)(width) = area. Find the area of each small rectangle inside the generic rectangle.

The total area of the generic rectangle, or $x^2−1$.

2. $2x(x + 1)(x + 1)$

First, multiply $2x$ and $(x+1)$.Then use a generic rectangle to multiply that result by $(x+1)$.

$2x^3+4x^2+2x$

3. $(x − 1)(x + 1)(x − 2)$

$(x^2−1)(x−2)$
Now use a generic rectangle.

4. Find the $x$- and $y$-intercepts of $y = x^3 − 2x^2 − x + 2$. The factors in part (c) should be useful.

The $x$-intercepts are where $y=0$.

$0=x^3−2x^2−x+2$

The $y$-intercept is where $x=0$:

$y=0^3−2(0)^2−0+2$

$0=(x−1)(x+1)(x−2)$ from part (c).

Using the Zero Product Property: $x−1=0\ \ \text{or}\ \ x+1=0\ \ \text{or}\ \ x−2=0$

$x=1\ \ \text{or}\ \ x=−1\ \ \text{or}\ \ x=2$