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4. Type IV-Factorization using identities

Use the following identities to factorize the expressions.

\begin{array}{l} {(a + b)}^{2} = a^{2} + 2 ab + b^{2} \\ {(a - b)}^{2} = a^{2} - 2 ab + b^{2} \\ a^{2} - b^{2} = (a + b) (a - b) \\ {(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} \\ {(a - b)}^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} \\ a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) \\ a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) \end{array}

Example:

1) \(y^3+64\)

Let us write the above expression as \(y^3+4^3\).

Use the identity, \(a^3+b^3 = (a+b)(a^2-ab+b^2)\).

y^{3} + 4^{3} = (y + 4) (y^{2} - y (4) + 4^{2})

y^{3} + 4^{3} = (y + 4) (y^{2} - 4 y + 16)

2) \(9x^2 -16y^2\)

Let us write the above expression as \((3x)^2-(4y)^2\).

Use the identity, \(a^2-b^2\) \(=\) \((a+b)(a-b)\).

\((3x)^2-(4x)^2\) \(=\) \((3x+4y)(3x-4y)\).

Did you find an error?