Let’s solve each problem step by step. We’re multiplying two binomials (expressions with two terms) using the distributive property — often called FOIL (First, Outer, Inner, Last). But we’ll just do it simply: multiply every term in the first parentheses by every term in the second.
---
Problem 1: (x + 4)(x + 7)
Multiply:
- x · x = x²
- x · 7 = 7x
- 4 · x = 4x
- 4 · 7 = 28
Now combine like terms:
7x + 4x = 11x
So answer:
x² + 11x + 28
---
Problem 2: (x + 9)(x - 2)
Multiply:
- x · x = x²
- x · (-2) = -2x
- 9 · x = 9x
- 9 · (-2) = -18
Combine like terms:
-2x + 9x = 7x
Answer:
x² + 7x - 18
---
Problem 3: (x - 5)(x + 6)
Multiply:
- x · x = x²
- x · 6 = 6x
- (-5) · x = -5x
- (-5) · 6 = -30
Combine like terms:
6x - 5x = x
Answer:
x² + x - 30
---
Problem 4: (x - 4)(x - 1)
Multiply:
- x · x = x²
- x · (-1) = -x
- (-4) · x = -4x
- (-4) · (-1) = 4
Combine like terms:
-x - 4x = -5x
Answer:
x² - 5x + 4
---
Problem 5: (2x - 10)(x + 3)
Multiply:
- 2x · x = 2x²
- 2x · 3 = 6x
- (-10) · x = -10x
- (-10) · 3 = -30
Combine like terms:
6x - 10x = -4x
Answer:
2x² - 4x - 30
---
Final Answer:
1. x² + 11x + 28
2. x² + 7x - 18
3. x² + x - 30
4. x² - 5x + 4
5. 2x² - 4x - 30
Parent Tip: Review the logic above to help your child master the concept of multiplying polynomials worksheet algebra 1.
