You’ve uploaded a worksheet titled
“Multiply a binomial by a monomial or a binomial — Positive Binomial Form”. The task is to
multiply each expression and write the result in
binomial form (i.e., simplified as a polynomial with two terms, if possible).
Let’s solve each problem step-by-step.
---
Problem 1: (x - 2)(x + 7)
Use FOIL (First, Outer, Inner, Last):
- First: x·x = x²
- Outer: x·7 = 7x
- Inner: -2·x = -2x
- Last: -2·7 = -14
Combine like terms:
x² + 7x - 2x - 14 =
x² + 5x - 14
✔ Answer: x² + 5x - 14
---
Problem 2: 8x(x - 7)
Distribute 8x to both terms inside the parentheses:
8x·x = 8x²
8x·(-7) = -56x
✔ Answer: 8x² - 56x
---
Problem 3: (x + 3)(x + 6)
FOIL:
- First: x·x = x²
- Outer: x·6 = 6x
- Inner: 3·x = 3x
- Last: 3·6 = 18
Combine: x² + 6x + 3x + 18 =
x² + 9x + 18
✔ Answer: x² + 9x + 18
---
Problem 4: (x - 6)(2x + 5)
FOIL:
- First: x·2x = 2x²
- Outer: x·5 = 5x
- Inner: -6·2x = -12x
- Last: -6·5 = -30
Combine: 2x² + 5x - 12x - 30 =
2x² - 7x - 30
✔ Answer: 2x² - 7x - 30
---
Problem 5: (x + 5)(x - 9)
FOIL:
- First: x·x = x²
- Outer: x·(-9) = -9x
- Inner: 5·x = 5x
- Last: 5·(-9) = -45
Combine: x² - 9x + 5x - 45 =
x² - 4x - 45
✔ Answer: x² - 4x - 45
---
Problem 6: (x + 4)(x - 8)
FOIL:
- First: x·x = x²
- Outer: x·(-8) = -8x
- Inner: 4·x = 4x
- Last: 4·(-8) = -32
Combine: x² - 8x + 4x - 32 =
x² - 4x - 32
✔ Answer: x² - 4x - 32
---
Problem 7: (x + 1)(2x + 4)
FOIL:
- First: x·2x = 2x²
- Outer: x·4 = 4x
- Inner: 1·2x = 2x
- Last: 1·4 = 4
Combine: 2x² + 4x + 2x + 4 =
2x² + 6x + 4
✔ Answer: 2x² + 6x + 4
---
Problem 8: x(2x + 6)
Distribute x:
x·2x = 2x²
x·6 = 6x
✔ Answer: 2x² + 6x
---
Problem 9: (x - 5)(x - 6)
FOIL:
- First: x·x = x²
- Outer: x·(-6) = -6x
- Inner: -5·x = -5x
- Last: -5·(-6) = 30
Combine: x² - 6x - 5x + 30 =
x² - 11x + 30
✔ Answer: x² - 11x + 30
---
Problem 10: x(x - 8)
Distribute x:
x·x = x²
x·(-8) = -8x
✔ Answer: x² - 8x
---
##
✔ Final Answers:
| Problem | Answer |
|---------|--------------------|
| 1 | x² + 5x - 14 |
| 2 | 8x² - 56x |
| 3 | x² + 9x + 18 |
| 4 | 2x² - 7x - 30 |
| 5 | x² - 4x - 45 |
| 6 | x² - 4x - 32 |
| 7 | 2x² + 6x + 4 |
| 8 | 2x² + 6x |
| 9 | x² - 11x + 30 |
| 10 | x² - 8x |
---
💡
Note: Although the worksheet says “Positive Binomial Form,” some answers have negative terms — that’s normal when multiplying binomials with subtraction. The term “positive binomial form” may refer to the structure of the input expressions (with positive leading coefficients), not the output.
Let me know if you’d like to see these worked out visually or need help graphing or factoring them next!
Parent Tip: Review the logic above to help your child master the concept of multiplying binomials worksheet with answers pdf.
