Answer:
The product is -x³ - 2x² + 13x + 26
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