Question

(y-11)-10(y-11)

1. $18b^{2}-49b+10$

Explanation:

Step1: Identify coefficients for AC method

For $18b^2 - 49b + 10$, $a=18$, $b=-49$, $c=10$. Calculate $a \times c = 18 \times 10 = 180$.

Step2: Find factor pair of 180

Find two numbers that multiply to 180 and add to -49: $-45$ and $-4$.

Step3: Split middle term

Rewrite the trinomial by splitting $-49b$:
$18b^2 - 45b - 4b + 10$

Step4: Factor by grouping

Group terms and factor out GCFs:
$9b(2b - 5) - 2(2b - 5)$

Step5: Factor out common binomial

Extract the shared binomial factor $(2b - 5)$:
$(9b - 2)(2b - 5)$

Answer:

$(9b - 2)(2b - 5)$