
Formulas: (a+b)^{2} = (a+b)(a+b) =a^{2}+2ab+b^{2} (ab)^{2} = (ab)(ab) =a^{2}2ab+b^{2} (a+b)^{3} = (a+b)(a+b)(a+b) = (a+b)(a^{2}+2ab+b^{2}) =a^{3}+3ab^{2}+3a^{2}b+b^{3} (ab)^{3} = (ab)(ab)(ab) = (ab)(a^{2}2ab+b^{2}) =a^{3}+3ab^{2}3a^{2}b+b^{3} Sum of squares: a^{2}+b^{2 }=(a+b)^{2} 2ab a^{2}+b^{2 }=(ab)^{2}+ 2ab Difference of squares: a^{2}b^{2 }=^{ }(a+b)(ab) Sum of cubes: a^{3} + b^{3} = (a^{2}  ab + b^{2})(a + b) Difference of cubes: a^{3}  b^{3} = (a^{2} + ab + b^{2})(a  b) Directions: Solve the following problems. Also write at least two examples for each formula above. 