Evaluate (x + 1)2 − (x − 1)2
A. 4x2
B. 2x−2
C. 4x
D. 4(1+x)
To evaluate the expression (x + 1)2 − (x − 1)2, we can expand the squares and simplify the expression.
Expanding the first square, we get:
(x + 1)2 = x2 + 2x + 1
Expanding the second square, we get:
(x − 1)2 = x2 − 2x + 1
Substituting these values back into the expression, we have:
(x + 1)2 − (x − 1)2 = (x2 + 2x + 1) − (x2 − 2x + 1)
Simplifying this expression, we have:
(x2 + 2x + 1) − (x2 − 2x + 1) = x2 + 2x + 1 − x2 + 2x - 1
Combining like terms, we have:
x2 - x2 + 2x + 2x + 1 - 1 = 4x
Therefore, the correct answer is C. 4x.
To evaluate (x + 1)2 − (x − 1)2, we can expand the square terms using the formula (a + b)2 = a2 + 2ab + b2.
Expanding (x + 1)2:
(x + 1)2 = x2 + 2(x)(1) + 1 = x2 + 2x + 1
Expanding (x − 1)2:
(x − 1)2 = x2 + 2(x)(-1) + (-1)2 = x2 - 2x + 1
Now subtracting (x − 1)2 from (x + 1)2:
(x + 1)2 − (x − 1)2 = (x2 + 2x + 1) − (x2 - 2x + 1)
Removing the parentheses and combining like terms:
(x2 + 2x + 1) - (x2 - 2x + 1) = x2 + 2x + 1 - x2 + 2x - 1
Simplifying the expression further:
x2 + x2 + 2x + 2x + 1 - 1 = 2x2 + 4x
Therefore, the answer is 2x2 + 4x, which corresponds to option B.