1. Find the product (13 - x2) (x + 2).

-x3 - 2x2 + 13x + 26

The product is - x³ - 2x² + 13x + 26

Step-by-step explanation:

* Lets revise how to find the product of two binomials

- If (ax ± b) and (cx ± d) are two binomials, where a, b, c, d are constant

their product is:

# Multiply (ax) by (cx) ⇒ 1st term in the 1st binomial and 1st term in the

2nd binomial

# Multiply (ax) by (d) ⇒ 1st term in 1st binomial and 2nd term in

2nd binomial

# Multiply (b) by (cx) ⇒ 2nd term in 1st binomial and 1st term in

2nd binomial

# Multiply (b) by (d) ⇒ 2nd term in 1st binomial and 2nd term in

2nd binomial

# (ax ± b) (cx ± d) = cx² ± adx ± bcx ± bd

- Add the terms adx and bcx because they are like terms

* Now lets solve the problem

- There are two binomials (13 - x²) and (x + 2)

- We can find their product by the way above

∵ (13) (x) = 13x ⇒ 1st term in the 1st binomial and 1st term in the

2nd binomial

∵ (13) (2) = 26 ⇒ 1st term in 1st binomial and 2nd term in

2nd binomial

∵ (-x²) (x) = - x³ ⇒ 2nd term in 1st binomial and 1st term in

2nd binomial

∵ (-x²) (2) = - 2x² ⇒ 2nd term in 1st binomial and 2nd term in

2nd binomial

∴ The product of (13 - x²) (x + 2) = 13x + 26 - x³ - 2x²

- There is no like terms

- Lets arrange the terms from greatest power to smallest power

∴ The product is - x³ - 2x² + 13x + 26