What is the factored form of b(2) + 12b + 32?

Question

luigi0210 · Answer

Do you mean: $b^2+12b+32$?

anonymous · Answer

yes

anonymous · Answer

(b-8) (b-4)

anonymous · Answer

This is a FOIL problem in reverse.$$ b^2 + 12b + 32=(b+8)(b+4)$$

luigi0210 · Answer

You guys might want to expand on that.

anonymous · Answer

The eight and four multiply to 32 and add to 12.

anonymous · Answer

how do I solve this not just the answer

anonymous · Answer

ok thankyou

luigi0210 · Answer

@AnimalAin Just gave a small explanation on how.

anonymous · Answer

can you guys help me on another one

anonymous · Answer

Sure.

anonymous · Answer

What is the factored form of 4k2 + 20k + 25?

anonymous · Answer

This one is a little more complicated.  We need to use the ac method, since the leading coefficient (in this case, four) isn't one.  Remember our general representation of a quadratic function y = ax^2 + bx + c 

First, find the product of a and c.  In this problem, that would be four times twenty-five, which equals 100.  Now find the factorization of 100 that adds to twenty.  I think it is ten and ten ( 10 times 10 is 100; 10 + 10 = 20).  Rewrite the expression as follows:$$4k^2 + 20k + 25=4k^2 + 10k+10k + 25$$Now factor by grouping.

anonymous · Answer

$$4k^2 + 20k + 25=4k2 + 10k+10k + 25=2k(2k +5)+5(2k +5)=(2k+5)^2$$

anonymous · Answer

Actually, if I had been more observant, I would have recognized that it was a perfect square at the start, and saved myself a bunch of work.  Live and learn...