1Cademy - Factoring $$a^2 - 11ab + 10b^2$$

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Factoring Trinomials of the Form $x^2 + bxy + cy^2$

Example

Factoring $a^2 - 11ab + 10b^2$

To factor the trinomial $a^2 - 11ab + 10b^2$ , find two factors that multiply to the constant term $10b^2$ and add to the middle term $-11ab$ . The terms in the binomials will begin with $a$ and end with $b$ . Since the last term is positive and the middle term is negative, both numerical coefficients must be negative. The negative factor pairs of $10$ are $-1, -10$ and $-2, -5$ . The pair $-1$ and $-10$ adds up to $-11$ . Therefore, use $-1$ and $-10$ as the coefficients for $b$ in the binomials. The factored form is $(a - b)(a - 10b)$ . We can check the result by multiplying: $(a - b)(a - 10b) = a^2 - 10ab - ab + 10b^2 = a^2 - 11ab + 10b^2$ .