substitution

Question

a=5, b=-2, x=p+1,

substitute and simplify

2x²-2(p²+1)

Answer 1

2x²-2(p²+1)

 

Quick note: the above method is correct, but (p + 1)² = p² + 2p + 1, not p² + 2p + 2.

 

So that gives you: 2(p² + 2p + 1) - 2(p² + 1)

 

I find distributing the 2's across the parentheses the easier method, just be sure to make note of any negative signs:

 

2p² + 4p + 2 - 2p² -2, which simplifies to 4p.

Answer 2

Your only real substitution in this problem is x->p+1, giving you

2(p+1)²-2(p²+1)

1) FOIL the first parentheses to give you

2(p²+2p+2)-2(p²+1)

2) Then you can group the two sets of parentheses before multiplying through, to have

2(p²+2p+2-(p²+1))

3) add like terms to get

2(2p+1)

4) And then multiple through to yield

4p+2

 

Alternately, after step 1 you can multiply both 2s through their respective parentheses, which will give you

2p²+4p+4-2p²-2

And once you group like terms you will once again get

4p+2