Polynomial Power Practice Notes
Multiplying Polynomials: Guided Practice Notes
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Name:
Date:
Period:
TYPE 1: STANDARD BINOMIALS Distributive / Area Model
\( (x + a)(x + b) \)
TYPE 2: COEFFICIENTS Distributive / Area Model
\( (ax + b)(cx + d) \)
[ I DO #1 ] \( (a + 10)(a - 2) \)
[ I DO #1 ] \( (2x + 1)(x - 7) \)
[ I DO #2 ] \( (x - 8)(x - 3) \)
[ I DO #2 ] \( (3n - 4)(2n + 5) \)
[ YOU DO ] \( (y + 6)(y - 5) \)
[ YOU DO ] \( (4m + 3)(m - 2) \)
Multiplying Polynomials: Guided Practice Notes
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Name:
Date:
Period:
TYPE 3: BINOMIAL \(\times\) TRINOMIAL Distribute All
\( (x + a)(Ax^2 + Bx + C) \)
TYPE 4: SQUARE OF A SUM \( (a + b)^2 = a^2 + 2ab + b^2 \)
\( (ax + b)^2 \)
[ I DO #1 ] \( (x - 1)(x^2 - 5x - 3) \)
[ I DO #1 ] \( (2x + 4)^2 \)
[ I DO #2 ] \( (2w + 3)(w^2 - 4w + 2) \)
[ I DO #2 ] \( (3p + 5)^2 \)
[ YOU DO ] \( (x - 4)(x^2 + 3x - 5) \)
[ YOU DO ] \( (5k + 2)^2 \)
Multiplying Polynomials: Guided Practice Notes
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Name:
Date:
Period:
TYPE 5: SQUARE OF A DIFFERENCE \( (a - b)^2 = a^2 - 2ab + b^2 \)
\( (ax - b)^2 \)
TYPE 6: SUM \(\times\) DIFFERENCE \( (a + b)(a - b) = a^2 - b^2 \)
\( (a + b)(a - b) \)
[ I DO #1 ] \( (3y - 7)^2 \)
[ I DO #1 ] \( (x - 10)(x + 10) \)
[ I DO #2 ] \( (4x - 3)^2 \)
[ I DO #2 ] \( (3m + 5)(3m - 5) \)
[ YOU DO ] \( (2w - 9)^2 \)
[ YOU DO ] \( (4z - 7)(4z + 7) \)
Multiplying Polynomials: Binomial \(\times\) Polynomial Practice
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Name:
Date:
Period:
1. \( (x + 4)(x^2 - 3x + 2) \) Workspace
2. \( (x - 2)(x^2 + 5x - 4) \) Workspace
3. \( (2x + 3)(x^2 - 4x + 5) \) Workspace
4. \( (3x - 1)(2x^2 + x - 6) \) Workspace
5. \( (x - 5)(2x^2 - 3x + 7) \) Workspace
6. \( (4x + 1)(x^2 - 2x - 3) \) Workspace
Polynomial Power Answer Key
ANSWER KEY
Multiplying Polynomials: Guided Notes
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Teacher Reference • Standard Binomials & Coefficients
All solutions shown with expansion & standard form
TYPE 1: STANDARD BINOMIALS Distributive / Area Model
\( (x + a)(x + b) = x^2 + (a+b)x + ab \)
TYPE 2: COEFFICIENTS Distributive / Area Model
\( (ax + b)(cx + d) = acx^2 + (ad+bc)x + bd \)
[ I DO #1 ] \( (a + 10)(a - 2) \)
\( = a(a - 2) + 10(a - 2) \)
\( = a^2 - 2a + 10a - 20 \)
\( \mathbf{a^2 + 8a - 20} \)
[ I DO #1 ] \( (2x + 1)(x - 7) \)
\( = 2x(x - 7) + 1(x - 7) \)
\( = 2x^2 - 14x + x - 7 \)
\( \mathbf{2x^2 - 13x - 7} \)
[ I DO #2 ] \( (x - 8)(x - 3) \)
\( = x(x - 3) - 8(x - 3) \)
\( = x^2 - 3x - 8x + 24 \)
\( \mathbf{x^2 - 11x + 24} \)
[ I DO #2 ] \( (3n - 4)(2n + 5) \)
\( = 3n(2n + 5) - 4(2n + 5) \)
\( = 6n^2 + 15n - 8n - 20 \)
\( \mathbf{6n^2 + 7n - 20} \)
[ YOU DO ] \( (y + 6)(y - 5) \)
\( = y(y - 5) + 6(y - 5) \)
\( = y^2 - 5y + 6y - 30 \)
\( \mathbf{y^2 + y - 30} \)
[ YOU DO ] \( (4m + 3)(m - 2) \)
\( = 4m(m - 2) + 3(m - 2) \)
\( = 4m^2 - 8m + 3m - 6 \)
\( \mathbf{4m^2 - 5m - 6} \)
ANSWER KEY
Multiplying Polynomials: Guided Notes
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Teacher Reference • Binomial × Trinomial & Square of a Sum
All solutions shown with expansion & standard form
TYPE 3: BINOMIAL \(\times\) TRINOMIAL Distribute All
\( (x + a)(Ax^2 + Bx + C) \)
TYPE 4: SQUARE OF A SUM \( (a + b)^2 = a^2 + 2ab + b^2 \)
\( (ax + b)^2 \)
[ I DO #1 ] \( (x - 1)(x^2 - 5x - 3) \)
\( = x(x^2 - 5x - 3) - 1(x^2 - 5x - 3) \)
\( = x^3 - 5x^2 - 3x - x^2 + 5x + 3 \)
\( \mathbf{x^3 - 6x^2 + 2x + 3} \)
[ I DO #1 ] \( (2x + 4)^2 \)
\( = (2x)^2 + 2(2x)(4) + (4)^2 \)
\( = 4x^2 + 16x + 16 \)
\( \mathbf{4x^2 + 16x + 16} \)
[ I DO #2 ] \( (2w + 3)(w^2 - 4w + 2) \)
\( = 2w(w^2 - 4w + 2) + 3(w^2 - 4w + 2) \)
\( = 2w^3 - 8w^2 + 4w + 3w^2 - 12w + 6 \)
\( \mathbf{2w^3 - 5w^2 - 8w + 6} \)
[ I DO #2 ] \( (3p + 5)^2 \)
\( = (3p)^2 + 2(3p)(5) + (5)^2 \)
\( = 9p^2 + 30p + 25 \)
\( \mathbf{9p^2 + 30p + 25} \)
[ YOU DO ] \( (x - 4)(x^2 + 3x - 5) \)
\( = x(x^2 + 3x - 5) - 4(x^2 + 3x - 5) \)
\( = x^3 + 3x^2 - 5x - 4x^2 - 12x + 20 \)
\( \mathbf{x^3 - x^2 - 17x + 20} \)
[ YOU DO ] \( (5k + 2)^2 \)
\( = (5k)^2 + 2(5k)(2) + (2)^2 \)
\( = 25k^2 + 20k + 4 \)
\( \mathbf{25k^2 + 20k + 4} \)
ANSWER KEY
Multiplying Polynomials: Guided Notes
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Teacher Reference • Difference of Squares & Square of Difference
All solutions shown with expansion & standard form
TYPE 5: SQUARE OF A DIFFERENCE \( (a - b)^2 = a^2 - 2ab + b^2 \)
\( (ax - b)^2 \)
TYPE 6: SUM \(\times\) DIFFERENCE \( (a + b)(a - b) = a^2 - b^2 \)
\( (a + b)(a - b) \)
[ I DO #1 ] \( (3y - 7)^2 \)
\( = (3y)^2 - 2(3y)(7) + (7)^2 \)
\( = 9y^2 - 42y + 49 \)
\( \mathbf{9y^2 - 42y + 49} \)
[ I DO #1 ] \( (x - 10)(x + 10) \)
\( = (x)^2 - (10)^2 \)
\( = x^2 - 100 \)
\( \mathbf{x^2 - 100} \)
[ I DO #2 ] \( (4x - 3)^2 \)
\( = (4x)^2 - 2(4x)(3) + (3)^2 \)
\( = 16x^2 - 24x + 9 \)
\( \mathbf{16x^2 - 24x + 9} \)
[ I DO #2 ] \( (3m + 5)(3m - 5) \)
\( = (3m)^2 - (5)^2 \)
\( = 9m^2 - 25 \)
\( \mathbf{9m^2 - 25} \)
[ YOU DO ] \( (2w - 9)^2 \)
\( = (2w)^2 - 2(2w)(9) + (9)^2 \)
\( = 4w^2 - 36w + 81 \)
\( \mathbf{4w^2 - 36w + 81} \)
[ YOU DO ] \( (4z - 7)(4z + 7) \)
\( = (4z)^2 - (7)^2 \)
\( = 16z^2 - 49 \)
\( \mathbf{16z^2 - 49} \)
ANSWER KEY
Binomial \(\times\) Polynomial Practice
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Teacher Reference • Full Expansion Solutions
All terms multiplied, combined, and boxed
1. \( (x + 4)(x^2 - 3x + 2) \)
\( = x(x^2 - 3x + 2) + 4(x^2 - 3x + 2) \)
\( = x^3 - 3x^2 + 2x + 4x^2 - 12x + 8 \)
\( \mathbf{x^3 + x^2 - 10x + 8} \)
2. \( (x - 2)(x^2 + 5x - 4) \)
\( = x(x^2 + 5x - 4) - 2(x^2 + 5x - 4) \)
\( = x^3 + 5x^2 - 4x - 2x^2 - 10x + 8 \)
\( \mathbf{x^3 + 3x^2 - 14x + 8} \)
3. \( (2x + 3)(x^2 - 4x + 5) \)
\( = 2x(x^2 - 4x + 5) + 3(x^2 - 4x + 5) \)
\( = 2x^3 - 8x^2 + 10x + 3x^2 - 12x + 15 \)
\( \mathbf{2x^3 - 5x^2 - 2x + 15} \)
4. \( (3x - 1)(2x^2 + x - 6) \)
\( = 3x(2x^2 + x - 6) - 1(2x^2 + x - 6) \)
\( = 6x^3 + 3x^2 - 18x - 2x^2 - x + 6 \)
\( \mathbf{6x^3 + x^2 - 19x + 6} \)
5. \( (x - 5)(2x^2 - 3x + 7) \)
\( = x(2x^2 - 3x + 7) - 5(2x^2 - 3x + 7) \)
\( = 2x^3 - 3x^2 + 7x - 10x^2 + 15x - 35 \)
\( \mathbf{2x^3 - 13x^2 + 22x - 35} \)
6. \( (4x + 1)(x^2 - 2x - 3) \)
\( = 4x(x^2 - 2x - 3) + 1(x^2 - 2x - 3) \)
\( = 4x^3 - 8x^2 - 12x + x^2 - 2x - 3 \)
\( \mathbf{4x^3 - 7x^2 - 14x - 3} \)
