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Special products worksheets Grades 8–9

Square a binomial and multiply a sum by a difference with the special product patterns.

The front of the free special products worksheet
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Free · Worked example · 21 problems · Answer key · US Letter

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How to do it

(a + b)² = a² + 2ab + b². (a + b)(a − b) = a² − b².

(4x+5)2=(4x)2+2(4x)(5)+52=16x2+40x+25(4x + 5)^{2} = (4x)^{2} + 2(4x)(5) + 5^{2} = 16x^{2} + 40x + 25(a + b)² = a² + 2ab + b²

Example problems

  1. (3x+6)2=(3x + 6)^{2} =
  2. (2x−8)2=(2x - 8)^{2} =
  3. (x+9)(x−9)=(x + 9)(x - 9) =
  4. (3x+2)2=(3x + 2)^{2} =

Polynomials and factoring

  1. Exponent rules
  2. Adding and subtracting polynomials
  3. Multiplying a monomial by a polynomial
  4. Multiplying binomials (FOIL)
  5. Special products
  6. Factoring out the GCF
  7. Factoring trinomials
  8. Factoring trinomials with a leading coefficient
  9. Factoring the difference of squares