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Polynomial Multiplication Examples and Solutions

Learn how to multiply polynomials vertically and horizontally with step-by-step examples and solutions. Practice finding products of binomials and using special product patterns.

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Polynomial Multiplication Examples and Solutions

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  1. a. Multiply – 2y2 + 3y – 6 andy – 2 in a vertical format. b. Multiplyx + 3 and 3x2 – 2x + 4 in a horizontal format. a. – 2y2 + 3y – 6 y –2 4y2 – 6y + 12 –2y3 +7y2 –12y + 12 EXAMPLE 3 Multiply polynomials vertically and horizontally SOLUTION Multiply – 2y2 + 3y – 6 by – 2 . –2y3 + 3y2 – 6y Multiply – 2y2 + 3y – 6 by y Combine like terms.

  2. EXAMPLE 3 Multiply polynomials vertically and horizontally b.(x + 3)(3x2 – 2x + 4) = (x + 3)3x2 –(x + 3)2x +(x + 3)4 = 3x3 + 9x2 – 2x2 – 6x + 4x + 12 = 3x3 + 7x2 – 2x + 12

  3. EXAMPLE 4 Multiply three binomials Multiply x – 5, x + 1, and x + 3 in a horizontal format. (x – 5)(x + 1)(x+ 3)= (x2– 4x – 5)(x + 3) = (x2– 4x – 5)x +(x2– 4x – 5)3 = x3 – 4x2 – 5x + 3x2 – 12x – 15 = x3 – x2 – 17x – 15

  4. EXAMPLE 5 Use special product patterns a. (3t + 4)(3t – 4) = (3t)2 – 42 Sum and difference = 9t2 – 16 b. (8x – 3)2 = (8x)2 – 2(8x)(3) + 32 Square of a binomial = 64x2 – 48x + 9 Cube of abinomial c. (pq + 5)3 = (pq)3 + 3(pq)2(5) + 3(pq)(5)2 + 53 = p3q3 + 15p2q2 + 75pq + 125

  5. 3x2 – x – 5 x + 2 3x3 + 5x2 – 7x – 10 for Examples 3, 4 and 5 GUIDED PRACTICE Find the product. 3. (x + 2)(3x2 – x – 5) SOLUTION Multiply 3x2 – x – 5 by 2 . 6x2 – 2x – 10 3x3 – x2 – 5x Multiply 3x2 – x – 5 by x. Combine like terms.

  6. for Examples 3, 4 and 5 GUIDED PRACTICE 4. (a – 5)(a + 2)(a + 6) SOLUTION (a – 5)(a + 2)(a + 6) = (a2 – 3a – 10)(a + 6) = (a2 – 3a – 10)a + (a2 – 3a – 10)6 = (a3 – 3a2 – 10a + 6a2 – 18a – 60) = (a3 + 3a2 – 28a – 60)

  7. for Examples 3, 4 and 5 GUIDED PRACTICE 5. (xy – 4)3 SOLUTION (xy – 4)3 = (xy)3 – 3(xy)2 + 3(xy)(4)2 – (4)3 = x3y3 – 12x2y2 + 48xy – 64

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