Expand the following formulas
$(a + b)^{2}$ =?
$(a - b)^{2}$ =?
$(a^{2} + b^{2})$ =?
$(a + b)^{3}$ =?
$(a - b)^{3}$ =?
$a^{3} + b^{3}$ =?
$a^{3} - b^{3}$ =?

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Solution

${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$
$(a^{2} + b^{2}) = {(a + b)}^{2} - 2 a b$
$= {(a - b)}^{2} + 2 a b$
${(a + b)}^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$= a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$
${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$= a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$
$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$
$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

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\infty (| a | < 1)

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Expand the following formulas(a+b)2=?(a−b)2=?(a2+b2)=?(a+b)3=?(a−b)3=?a3+b3=?a3−b3=?

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Expand the following formulas
$(a + b)^{2}$ =?
$(a - b)^{2}$ =?
$(a^{2} + b^{2})$ =?
$(a + b)^{3}$ =?
$(a - b)^{3}$ =?
$a^{3} + b^{3}$ =?
$a^{3} - b^{3}$ =?