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Product To Sum IdentitiesDescription \(\cos{x}\cos{y} = \frac{1}{2}(\cos{(x+y)}+\cos{(x-y)})\) \(\sin{x}\sin{y} = \frac{1}{2}(\cos{(x-y)}-\cos{(x+y)})\) \(\sin{x}\cos{y} = \frac{1}{2}(\sin{(x+y)}+\cos{(x-y)})\) |
Examples \[{x}^{3}+6{x}^{2}+12x+8\] 1 Rewrite it in the form \({a}^{3}+3{a}^{2}b+3a{b}^{2}+{b}^{3}\), where \(a=x\) and \(b=2\). \[{x}^{3}+3{x}^{2}(2)+3(x)\times {2}^{2}+{2}^{3}\] 2 Use Cube of Sum: \({(a+b)}^{3}={a}^{3}+3{a}^{2}b+3a{b}^{2}+{b}^{3}\). \[{(x+2)}^{3}\] Done  |