a^{2} - b^{2}

=

(a + b)(a - b)

a^{2} + 2ab + b^{2}

(a + b)(a + b)

a^{2} - 2ab + 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^{3} + 3a^{2}b + 3ab^{2} + b^{3}

(a + b)^{3}

a^{3} - 3a^{2}b + 3ab^{2} - b^{3}

(a - b)^{3}

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