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The following Polynomial Factorization formulae are useful when trying to factor any polynomials. In math, it is useful to know some important formulae to help you solve math problems. You should be familiar with the polynomial factorization formulae below. Although, when each polynomial factorization equation is common sense when you multiply them out, it is useful to be able to recognize the common standard polynomial factorization equations such as those below. 

a ( c+d ) = ac + ad

(a + b)(a – b) = a 2 – b 2

(a + b)(a + b) = (a + b) 2 = a 2 + 2ab + b 2

(a – b)(a – b) = (a – b) 2 = a 2 – 2ab + b 2

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• (x + a)(x + b) = x ² + (a + b)x + ab
• (ax + b)(cx + d) = acx ² + (ad + bc)x + bd
• (a + b)(a + b)(a + b) = (a + b) ³ = a ³ + 3a ² b + 3ab ² + b ³ 
• (a – b)(a – b)(a – b) = (a – b) ³ = a ³ – 3a ² b + 3ab ² – b ³

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• (a – b)(a ² + ab + b ²) = a ³ - b ³
• (a + b)(a ² – ab + b ²) = a ³ + b ³
• (a + b + c) ² = a ² + b ² + c ² + 2ab + 2ac + 2bc
• (a – b)(a ³ + a ² b + ab ² + b ³) = a ⁴ - b ⁴
• (a – b)(a ⁴ + a ³ b + a ² b ² + ab ³ + b ⁴) = a ⁵ - b ⁵

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• Polynomial Factorization