Sure, let's go ahead and factor the expression 2(3–b)+5(b–3)^2.
Step 1: Rewrite the expression with a common factor
The expression is 2(3–b)+5(b–3)^2. We can see that (b-3) is a common factor. But be careful here, the sign in front of b is not the same in the both instances. To make it the same, we can rewrite 2(3–b) as -2(b-3). Therefore, the expression becomes -2(b-3)+5(b–3)^2.
Step 2: Factor out the common element
Now that we have (b-3) as a common factor in both terms, we can factor it out. When we factor out (b-3) from both terms, the expression becomes (b-3)[-2+5(b-3)].
Step 3: Simplify the Expression
You can further simplify the expression by multiplying 5 with (b-3) in the second term of the expression inside the brackets. You get (b-3)(5b -15 - 2) which can be simplified further to (2+5*(b-3))*(b-3).
So the expression 2(3–b)+5(b–3)^2 is equal to (2+5*(b-3))*(b-3) when written as a product of two polynomials.