Question

Simplify the following polynomials.
7. (2x+3)(x+1)
10. (w+6)(3w-4)
11. (5x+3)(x-2)

Answer 1

Let's simplify each of the given polynomials one by one:

**7. (2x + 3)(x + 1)**

To simplify, we'll use the distributive property (also known as the FOIL method for binomials):

\[
(2x + 3)(x + 1) = 2x \cdot x + 2x \cdot 1 + 3 \cdot x + 3 \cdot 1
\]
\[
= 2x^2 + 2x + 3x + 3
\]
Combine like terms:
\[
= 2x^2 + 5x + 3
\]

**10. (w + 6)(3w - 4)**

Using the distributive property:

\[
(w + 6)(3w - 4) = w \cdot 3w + w \cdot (-4) + 6 \cdot 3w + 6 \cdot (-4)
\]
\[
= 3w^2 - 4w + 18w - 24
\]
Combine like terms:
\[
= 3w^2 + 14w - 24
\]

**11. (5x + 3)(x - 2)**

Using the distributive property:

\[
(5x + 3)(x - 2) = 5x \cdot x + 5x \cdot (-2) + 3 \cdot x + 3 \cdot (-2)
\]
\[
= 5x^2 - 10x + 3x - 6
\]
Combine like terms:
\[
= 5x^2 - 7x - 6
\]

So, the simplified forms are:

- **7.** \(2x^2 + 5x + 3\)
- **10.** \(3w^2 + 14w - 24\)
- **11.** \(5x^2 - 7x - 6\)