Carcass wrote:
(2x+1)2−(2x−1)2=
A. 2
B. 8x
C. 4x-1
D. 4x+1
E. 8x+2
Here's another approach:
We are looking for an algebraic expression that is equivalent to the expression
(2x+1)2−(2x−1)2 So, the value of
(2x+1)2−(2x−1)2 for a given value of x should be equal if the correct answer when evaluated for the same value of x.
Here's what I mean:
If x = 3, then
(2x+1)2−(2x−1)2=[2(3)+1]2−[2(3)−1]2=[6+1]2−[6−1]2=72−52=49+25=24So, when x = 3,
(2x+1)2−(2x−1)2=24This means the correct answer will be the one that evaluates to equal 24, when x =
3Let's past each answer choice
A. 2 NO GOOD.
B. 8(
3) = 24 KEEP
C. 4(
3) - 1 = 11 NO GOOD.
D. 4(
3) + 1 = 13 NO GOOD.
E. 8(
3) + 2 = 26 NO GOOD.
Answer: B
ASIDE: The above strategy is very useful in situations in which you don't know how to perform the algebraic steps necessary to simplify the given expression
Cheers,
Brent