Polynomial Products Guided Notes Multiplying Polynomials: Guided Practice Notes
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Example Type 1: Standard Binomials \((x + a)(x + b)\) Distributive Property / Area Model
[ I DO #1 ]\((a + 10)(a - 2)\)
[ I DO #2 ]\((x - 8)(x - 3)\)
[ YOU DO ]\((y + 6)(y - 5)\)
Example Type 2: Binomials with Coefficients \((ax + b)(cx + d)\) Distributive Property / Area Model
[ I DO #1 ]\((2x + 1)(x - 7)\)
[ I DO #2 ]\((3n - 4)(2n + 5)\)
[ YOU DO ]\((4m + 3)(m - 2)\)
Multiplying Polynomials — Guided Practice Page 1 of 4
Multiplying Polynomials: Guided Practice Notes
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Example Type 3: Binomial \(\times\) Trinomial \((x + a)(Ax^2 + Bx + C)\) Distribute Each Term Across All Three
[ I DO #1 ]\((x - 1)(x^2 - 5x - 3)\)
[ I DO #2 ]\((2w + 3)(w^2 - 4w + 2)\)
[ YOU DO ]\((x - 4)(x^2 + 3x - 5)\)
Example Type 4: Square of a Sum \((ax + b)^2\) Pattern: \((a + b)^2 = a^2 + 2ab + b^2\)
[ I DO #1 ]\((2x + 4)^2\)
[ I DO #2 ]\((3p + 5)^2\)
[ YOU DO ]\((5k + 2)^2\)
Multiplying Polynomials — Guided Practice Page 2 of 4
Multiplying Polynomials: Guided Practice Notes
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Example Type 5: Square of a Difference \((ax - b)^2\) Pattern: \((a - b)^2 = a^2 - 2ab + b^2\)
[ I DO #1 ]\((3y - 7)^2\)
[ I DO #2 ]\((4x - 3)^2\)
[ YOU DO ]\((2w - 9)^2\)
Example Type 6: Sum \(\times\) Difference \((a + b)(a - b)\) Pattern: \((a + b)(a - b) = a^2 - b^2\)
[ I DO #1 ]\((x - 10)(x + 10)\)
[ I DO #2 ]\((3m + 5)(3m - 5)\)
[ YOU DO ]\((4z - 7)(4z + 7)\)
Multiplying Polynomials — Guided Practice Page 3 of 4
Multiplying Polynomials: Binomial × Polynomial Practice
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1.\((x + 4)(x^2 - 3x + 2)\)
2.\((x - 2)(x^2 + 5x - 4)\)
3.\((2x + 3)(x^2 - 4x + 5)\)
4.\((3x - 1)(2x^2 + x - 6)\)
5.\((x - 5)(2x^2 - 3x + 7)\)
6.\((4x + 1)(x^2 - 2x - 3)\)
Multiplying Polynomials — Binomial \(\times\) Polynomial Practice Page 4 of 4
Polynomial Mastery Practice Worksheet Multiplying Polynomials Practice
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1.\((x + 7)(x + 4)\)
2.\((p - 9)(p + 3)\)
3.\((2x + 5)(x + 3)\)
4.\((3a - 2)(2a + 7)\)
5.\((x - 1)(x^2 - 5x - 3)\)
6.\((2x + 3)(x^2 - 4x + 2)\)
Multiplying Polynomials Practice Page 1 of 2
Multiplying Polynomials Practice
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Date: __________________
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7.\((x + 3)(x^2 - 4x + 6)\)
8.\((2y - 1)(3y^2 + 2y - 4)\)
9.\((2x + 4)^2\)
10.\((3y - 7)^2\)
11.\((x - 10)(x + 10)\)
12.\((2a + 7)(2a - 7)\)
Multiplying Polynomials Practice Page 2 of 2
Polynomial Products Answer Key TEACHER KEY
Polynomial Products Answer Key
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Solutions for Guided Notes "You Do" (Pages 1–3) and Practice (Page 4).
Guided Notes: "You Do" Solutions (Pages 1–3)
Type 1: \((y + 6)(y - 5)\)
\(y^2 - 5y + 6y - 30\)
Answer: \(y^2 + y - 30\)
Type 2: \((4m + 3)(m - 2)\)
\(4m^2 - 8m + 3m - 6\)
Answer: \(4m^2 - 5m - 6\)
Type 3: \((x - 4)(x^2 + 3x - 5)\)
\(x^3 + 3x^2 - 5x - 4x^2 - 12x + 20\)
Answer: \(x^3 - x^2 - 17x + 20\)
Type 4: \((5k + 2)^2\)
\((5k)^2 + 2(5k)(2) + 2^2\)
Answer: \(25k^2 + 20k + 4\)
Type 5: \((2w - 9)^2\)
\((2w)^2 - 2(2w)(9) + 9^2\)
Answer: \(4w^2 - 36w + 81\)
Type 6: \((4z - 7)(4z + 7)\)
\((4z)^2 - (7)^2\)
Answer: \(16z^2 - 49\)
Guided Notes: Binomial \(\times\) Polynomial Practice (Page 4) Solutions
1. \((x + 4)(x^2 - 3x + 2)\)
\(x^3 - 3x^2 + 2x + 4x^2 - 12x + 8\)
Answer: \(x^3 + x^2 - 10x + 8\)
2. \((x - 2)(x^2 + 5x - 4)\)
\(x^3 + 5x^2 - 4x - 2x^2 - 10x + 8\)
Answer: \(x^3 + 3x^2 - 14x + 8\)
3. \((2x + 3)(x^2 - 4x + 5)\)
\(2x^3 - 8x^2 + 10x + 3x^2 - 12x + 15\)
Answer: \(2x^3 - 5x^2 - 2x + 15\)
4. \((3x - 1)(2x^2 + x - 6)\)
\(6x^3 + 3x^2 - 18x - 2x^2 - x + 6\)
Answer: \(6x^3 + x^2 - 19x + 6\)
5. \((x - 5)(2x^2 - 3x + 7)\)
\(2x^3 - 3x^2 + 7x - 10x^2 + 15x - 35\)
Answer: \(2x^3 - 13x^2 + 22x - 35\)
6. \((4x + 1)(x^2 - 2x - 3)\)
\(4x^3 - 8x^2 - 12x + x^2 - 2x - 3\)
Answer: \(4x^3 - 7x^2 - 14x - 3\)
Teacher Answer Key — Polynomial Products Page 1 of 2
TEACHER KEY
Polynomial Products Answer Key
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Complete worked solutions for Practice Worksheet Problems 1–12.
Practice Worksheet: Page 1 Solutions (Problems 1–6)
1. \((x + 7)(x + 4)\)
\(x^2 + 4x + 7x + 28\)
Answer: \(x^2 + 11x + 28\)
2. \((p - 9)(p + 3)\)
\(p^2 + 3p - 9p - 27\)
Answer: \(p^2 - 6p - 27\)
3. \((2x + 5)(x + 3)\)
\(2x^2 + 6x + 5x + 15\)
Answer: \(2x^2 + 11x + 15\)
4. \((3a - 2)(2a + 7)\)
\(6a^2 + 21a - 4a - 14\)
