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Factoring Special Products — Easy Worksheet 1
Grade 9 · Whoobee Name: ____________________ Date: __________
Factor completely. Write a difference of squares like (x + 5)(x - 5) and a perfect square like (x + 5)^2.
How to solve
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Example
Factor: x² - 81
Answer: (x + 9)(x - 9)
Not quite. The answer is
💡 x² is the square of x and 16 is the square of 4, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 4: (x + 4)(x − 4). Check with FOIL: (x + 4)(x − 4) = x² − 4x + 4x − 16 = x² − 16; the middle terms cancel.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 16 is the square of 4, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 4: (x + 4)(x − 4). Check with FOIL: (x + 4)(x − 4) = x² − 4x + 4x − 16 = x² − 16; the middle terms cancel.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 25
✓ 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
💡 x² is the square of x and 64 is the square of 8. The middle term is +2 × x × 8 = +16x, so this is a perfect square trinomial. Use A² + 2AB + B² = (A + B)² with A = x and B = 8: (x + 8)². Check with FOIL: (x + 8)² = (x + 8)(x + 8) = x² + 8x + 8x + 64 = x² + 16x + 64.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 64 is the square of 8. The middle term is +2 × x × 8 = +16x, so this is a perfect square trinomial. Use A² + 2AB + B² = (A + B)² with A = x and B = 8: (x + 8)². Check with FOIL: (x + 8)² = (x + 8)(x + 8) = x² + 8x + 8x + 64 = x² + 16x + 64.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 25
✓ 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
💡 x² is the square of x and 100 is the square of 10, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 10: (x + 10)(x − 10). Check with FOIL: (x + 10)(x − 10) = x² − 10x + 10x − 100 = x² − 100; the middle terms cancel.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 100 is the square of 10, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 10: (x + 10)(x − 10). Check with FOIL: (x + 10)(x − 10) = x² − 10x + 10x − 100 = x² − 100; the middle terms cancel.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 64
✓ 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
💡 x² is the square of x and 1 is the square of 1. The middle term is +2 × x × 1 = +2x, so this is a perfect square trinomial. Use A² + 2AB + B² = (A + B)² with A = x and B = 1: (x + 1)². Check with FOIL: (x + 1)² = (x + 1)(x + 1) = x² + x + x + 1 = x² + 2x + 1.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 1 is the square of 1. The middle term is +2 × x × 1 = +2x, so this is a perfect square trinomial. Use A² + 2AB + B² = (A + B)² with A = x and B = 1: (x + 1)². Check with FOIL: (x + 1)² = (x + 1)(x + 1) = x² + x + x + 1 = x² + 2x + 1.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 9
✓ 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
💡 x² is the square of x and 25 is the square of 5, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 5: (x + 5)(x − 5). Check with FOIL: (x + 5)(x − 5) = x² − 5x + 5x − 25 = x² − 25; the middle terms cancel.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 25 is the square of 5, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 5: (x + 5)(x − 5). Check with FOIL: (x + 5)(x − 5) = x² − 5x + 5x − 25 = x² − 25; the middle terms cancel.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 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
💡 x² is the square of x and 4 is the square of 2. The middle term is +2 × x × 2 = +4x, so this is a perfect square trinomial. Use A² + 2AB + B² = (A + B)² with A = x and B = 2: (x + 2)². Check with FOIL: (x + 2)² = (x + 2)(x + 2) = x² + 2x + 2x + 4 = x² + 4x + 4.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 4 is the square of 2. The middle term is +2 × x × 2 = +4x, so this is a perfect square trinomial. Use A² + 2AB + B² = (A + B)² with A = x and B = 2: (x + 2)². Check with FOIL: (x + 2)² = (x + 2)(x + 2) = x² + 2x + 2x + 4 = x² + 4x + 4.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 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
💡 x² is the square of x and 36 is the square of 6, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 6: (x + 6)(x − 6). Check with FOIL: (x + 6)(x − 6) = x² − 6x + 6x − 36 = x² − 36; the middle terms cancel.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 36 is the square of 6, and the terms are subtracted, so this is a difference of squares. Use A² − B² = (A + B)(A − B) with A = x and B = 6: (x + 6)(x − 6). Check with FOIL: (x + 6)(x − 6) = x² − 6x + 6x − 36 = x² − 36; the middle terms cancel.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 81
✓ 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
💡 x² is the square of x and 25 is the square of 5. The middle term is −2 × x × 5 = −10x, so this is a perfect square trinomial. Use A² − 2AB + B² = (A − B)² with A = x and B = 5: (x − 5)². Check with FOIL: (x − 5)² = (x − 5)(x − 5) = x² − 5x − 5x + 25 = x² − 10x + 25.
✓ Correct!
Not quite. The answer is
💡 x² is the square of x and 25 is the square of 5. The middle term is −2 × x × 5 = −10x, so this is a perfect square trinomial. Use A² − 2AB + B² = (A − B)² with A = x and B = 5: (x − 5)². Check with FOIL: (x − 5)² = (x − 5)(x − 5) = x² − 5x − 5x + 25 = x² − 10x + 25.
💡 How to solve: Factoring Special Products
Difference of two squares: a2 - b2 = (a + b)(a - b). Perfect-square trinomial: a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2. Check that the first and last terms are perfect squares and, for a trinomial, that the middle term is 2ab.
Try a similar one
Factor: x² - 25
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Factoring Special Products — Easy Worksheet 1
Factor completely. Write a difference of squares like (x + 5)(x - 5) and a perfect square like (x + 5)^2.