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Multiplying Polynomials & Special Products — Easy Worksheet 1
Grade 9 · MathSheets Name: ____________________ Date: __________
Multiply. Write each answer in standard form (highest power first).
How to solve
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Example
-6x(3x² + 5x - 6)
Answer: -18x³ - 30x² + 36x
Not quite. The answer is
💡 Distribute: multiply −4x² by each term inside the parentheses. Multiply the coefficients and add the exponents of x: (−4x²) × 2x² = −8x4, (−4x²) × (−x) = 4x³, (−4x²) × 2 = −8x². So the answer is −8x4 + 4x³ − 8x².
✓ Correct!
Not quite. The answer is
💡 Distribute: multiply −4x² by each term inside the parentheses. Multiply the coefficients and add the exponents of x: (−4x²) × 2x² = −8x4, (−4x²) × (−x) = 4x³, (−4x²) × 2 = −8x². So the answer is −8x4 + 4x³ − 8x².
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
6x²(x² + 4x + 4)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use FOIL. First: 2x × 3x = 6x². Outer: 2x × 1 = 2x. Inner: 3 × 3x = 9x. Last: 3 × 1 = 3. Add them and combine like terms: 6x² + 2x + 9x + 3 = 6x² + 11x + 3.
✓ Correct!
Not quite. The answer is
💡 Use FOIL. First: 2x × 3x = 6x². Outer: 2x × 1 = 2x. Inner: 3 × 3x = 9x. Last: 3 × 1 = 3. Add them and combine like terms: 6x² + 2x + 9x + 3 = 6x² + 11x + 3.
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
6x(2x² - 3x - 4)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Squaring means multiplying it by itself: (3x − 3)2 = (3x − 3)(3x − 3). Use FOIL. First: 3x × 3x = 9x². Outer: 3x × (−3) = −9x. Inner: (−3) × 3x = −9x. Last: (−3) × (−3) = 9. Add them and combine like terms: 9x² − 9x − 9x + 9 = 9x² − 18x + 9.
✓ Correct!
Not quite. The answer is
💡 Squaring means multiplying it by itself: (3x − 3)2 = (3x − 3)(3x − 3). Use FOIL. First: 3x × 3x = 9x². Outer: 3x × (−3) = −9x. Inner: (−3) × 3x = −9x. Last: (−3) × (−3) = 9. Add them and combine like terms: 9x² − 9x − 9x + 9 = 9x² − 18x + 9.
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
3x(3x² - 6x - 5)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use FOIL. First: 2x × 2x = 4x². Outer: 2x × (−7) = −14x. Inner: 7 × 2x = 14x. Last: 7 × (−7) = −49. The outer and inner terms are opposites, so they cancel. Add them and combine like terms: 4x² − 14x + 14x − 49 = 4x² − 49.
✓ Correct!
Not quite. The answer is
💡 Use FOIL. First: 2x × 2x = 4x². Outer: 2x × (−7) = −14x. Inner: 7 × 2x = 14x. Last: 7 × (−7) = −49. The outer and inner terms are opposites, so they cancel. Add them and combine like terms: 4x² − 14x + 14x − 49 = 4x² − 49.
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
-4x²(3x² - 3x + 5)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Distribute: multiply 4x² by each term inside the parentheses. Multiply the coefficients and add the exponents of x: 4x² × x² = 4x4, 4x² × 5x = 20x³, 4x² × 6 = 24x². So the answer is 4x4 + 20x³ + 24x².
✓ Correct!
Not quite. The answer is
💡 Distribute: multiply 4x² by each term inside the parentheses. Multiply the coefficients and add the exponents of x: 4x² × x² = 4x4, 4x² × 5x = 20x³, 4x² × 6 = 24x². So the answer is 4x4 + 20x³ + 24x².
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
-5x(x² + 3x - 6)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use FOIL. First: 3x × x = 3x². Outer: 3x × (−5) = −15x. Inner: 5 × x = 5x. Last: 5 × (−5) = −25. Add them and combine like terms: 3x² − 15x + 5x − 25 = 3x² − 10x − 25.
✓ Correct!
Not quite. The answer is
💡 Use FOIL. First: 3x × x = 3x². Outer: 3x × (−5) = −15x. Inner: 5 × x = 5x. Last: 5 × (−5) = −25. Add them and combine like terms: 3x² − 15x + 5x − 25 = 3x² − 10x − 25.
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
3x(3x² - 2x + 1)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Squaring means multiplying it by itself: (x + 4)2 = (x + 4)(x + 4). Use FOIL. First: x × x = x². Outer: x × 4 = 4x. Inner: 4 × x = 4x. Last: 4 × 4 = 16. Add them and combine like terms: x² + 4x + 4x + 16 = x² + 8x + 16.
✓ Correct!
Not quite. The answer is
💡 Squaring means multiplying it by itself: (x + 4)2 = (x + 4)(x + 4). Use FOIL. First: x × x = x². Outer: x × 4 = 4x. Inner: 4 × x = 4x. Last: 4 × 4 = 16. Add them and combine like terms: x² + 4x + 4x + 16 = x² + 8x + 16.
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
3x²(3x² + 2x + 4)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use FOIL. First: 3x × 3x = 9x². Outer: 3x × (−1) = −3x. Inner: 1 × 3x = 3x. Last: 1 × (−1) = −1. The outer and inner terms are opposites, so they cancel. Add them and combine like terms: 9x² − 3x + 3x − 1 = 9x² − 1.
✓ Correct!
Not quite. The answer is
💡 Use FOIL. First: 3x × 3x = 9x². Outer: 3x × (−1) = −3x. Inner: 1 × 3x = 3x. Last: 1 × (−1) = −1. The outer and inner terms are opposites, so they cancel. Add them and combine like terms: 9x² − 3x + 3x − 1 = 9x² − 1.
💡 How to solve: Multiplying Polynomials & Special Products
Multiply every term of the first polynomial by every term of the second, then combine like terms. Special products: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2.
Try a similar one
5x²(3x² - 2x - 1)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Multiplying Polynomials & Special Products — Easy Worksheet 1
Multiply. Write each answer in standard form (highest power first).