Testinar Grade 8 math

Multiplying Binomials and Factoring Quadratics

Learn to reason about and solve Grade 8 problems involving Multiplying Binomials and Factoring Quadratics.

CH03-08 Equations, Inequalities, and Systems
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. The area of a rectangle with dimensions \((x+4)\) and \((x-4)\) is shown below. Which expression represents the area?

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q003
    1. \(x^2-8\)
    2. \(x^2+8x-16\)
    3. \(x^2-16\)
    4. \(2x-16\)

  2. The area model below represents \((x+2)(x+4)\): What is the total area?

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q009
    1. \(x^2+6x+8\)
    2. \(x^2+8\)
    3. \(x^2+4x+2\)
    4. \(2x^2+6x+8\)

  3. The area model represents \((x+5)^2\): What is the sum of all areas?

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q020
    1. \(x^2+10x+25\)
    2. \(x^2+25\)
    3. \(x^2+5x+5\)
    4. \(2x^2+10x\)

  4. A clue box for factoring the trinomial shows: Which expression completes the factorization?

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q035
    1. \((x+4)(x+5)\)
    2. \((x+9)(x+20)\)
    3. \((x-4)(x-5)\)
    4. \(x(x+4)(x+5)\)

  5. A garden is shaped like a rectangle with length \((2x+1)\) m and width \((x+3)\) m. What is its area in square meters?

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q036
    1. \(2x^2+7x+3\)
    2. \(2x^2+3x+7\)
    3. \(3x^2+4x+3\)
    4. \(2x^2+6x+3\)

  6. Factor \(x^2-14x+45\).

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q039
    1. \((x-5)(x-9)\)
    2. \((x-15)(x+1)\)
    3. \((x-10)(x-4)\)
    4. \((x-45)(x+1)\)

  7. Factor \(9x^2-36\) completely.

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q040
    1. \(9(x^2-4)\)
    2. \(9(x-2)(x+2)\)
    3. \((3x-6)^2\)
    4. \((x-6)(9x+6)\)

  8. An area model for \((x+6)(x-2)\) shows four rectangular regions. What is their total area?

    Multiplying Binomials and Factoring Quadratics visual for G8-C03-T08-Q042
    1. \(x^2+4x-12\)
    2. \(x^2-12\)
    3. \(x^2+8x-12\)
    4. \(x^2+6x-2\)
Teacher and parent reference

Answer key and explanations

  1. C. \(x^2-16\)

    Difference of squares: \((x+4)(x-4)=x^2-4^2=x^2-16\).

  2. A. \(x^2+6x+8\)

    Sum of areas: \(x^2+2x+4x+8=x^2+6x+8\).

  3. A. \(x^2+10x+25\)

    Sum: \(x^2+5x+5x+25=x^2+10x+25=(x+5)^2\).

  4. A. \((x+4)(x+5)\)

    Trinomial \(x^2+9x+20\) factors as \((x+4)(x+5)\) (multiply: \(4 \cdot 5=20\), add: \(4+5=9\)).

  5. A. \(2x^2+7x+3\)

    Area = \((2x+1)(x+3)=2x^2+6x+x+3=2x^2+7x+3\) m\(^2\).

  6. A. \((x-5)(x-9)\)

    Find two numbers that multiply to \(45\) and add to \(-14\): \(-5\) and \(-9\). Verify: \((-5)(-9)=45\) and \(-5-9=-14\).

  7. B. \(9(x-2)(x+2)\)

    Factor out GCF of \(9\): \(9(x^2-4)\). Then difference of squares: \(9(x-2)(x+2)\).

  8. A. \(x^2+4x-12\)

    Sum of regions: \(x^2+6x-2x-12=x^2+4x-12\).

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