Factoring and Product Formulas

Factoring Formulas

\( a^2 – b^2 = (a – b)(a + b) \)

\( a^3 – b^3 = (a – b)(a^2 + ab + b^2) \)

\( a^3 + b^3 = (a + b)(a^2 – ab + b^2) \)

\( a^4 – b^4 = (a – b)(a + b)(a^2 + b^2) \)

\( a^5 – b^5 = (a – b)(a^4 + a^3b + a^2b^2 + ab^3 + b^4) \)

Product Formulas

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

\( (a – b)^2 = a^2 – 2ab + b^2 \)

\( (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \)

\( (a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3 \)

\( (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 \)

\( (a – b)^4 = a^4 – 4a^3b + 6a^2b^2 – 4ab^3 + b^4 \)

\( (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc \)

\( (a + b + c + \dots)^2 = a^2 + b^2 + c^2 + \dots 2(ab + ac + bc + \dots) \)

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