1Cademy - Factoring $$16x^2 - 24xy + 9y^2

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Factoring by Grouping

Example

Factoring $16x^2 - 24xy + 9y^2 - 64$

Factor the polynomial $16x^2 - 24xy + 9y^2 - 64$ completely. Check for a greatest common factor. There is no overall GCF. Since there are $4$ terms, group the first $3$ terms together: $(16x^2 - 24xy + 9y^2) - 64$ . Identify the grouped trinomial as a perfect square trinomial that fits the pattern $a^2 - 2ab + b^2$ with $a = 4x$ and $b = 3y$ . Factor it into a squared binomial: $(4x - 3y)^2 - 64$ . The new expression is a difference of squares: $(4x - 3y)^2 - 8^2$ . Factor it as a product of conjugates: $((4x - 3y) - 8)((4x - 3y) + 8)$ . Simplify to yield the completely factored form: $(4x - 3y - 8)(4x - 3y + 8)$ . Verify the factored form by multiplying.