Which of the following is equivalent to the expression below?
(4 - x) (x + 2)
A.
x2 + 2x - 8
B.
x2 - 2x + 8
C.
-x2 +2x + 8
D.
-x2 - 2x - 8
To find the equivalent expression, we can distribute (4 - x) to the terms in (x + 2).
(4 - x)(x + 2) = 4(x) + 4(2) - x(x) - x(2)
= 4x + 8 - x^2 - 2x
= -x^2 + 2x + 4x + 8
= -x^2 + 6x + 8
Therefore, the equivalent expression is -x^2 + 6x + 8, which is option C.
To find the equivalent expression, we can use the distributive property.
First, distribute the 4 to both terms inside the parentheses:
(4 - x) (x + 2) = 4(x) + 4(2) - x(x) - x(2)
Simplify the expression:
= 4x + 8 - x^2 - 2x
Rearrange the terms in descending order of powers:
= -x^2 + 4x - 2x + 8
Combine like terms:
= -x^2 + 2x + 8
So, the equivalent expression is: -x^2 + 2x + 8
Therefore, the correct answer is option C.
To determine which option is equivalent to the expression (4 - x) (x + 2), let's multiply the two binomials together and simplify the result.
Start by multiplying the first terms of each binomial:
(4 - x) (x + 2) = 4x
Next, multiply the outer terms:
(4 - x) (x + 2) = -x * 2 = -2x
Then, multiply the inner terms:
(4 - x) (x + 2) = 4 * x = 4x
Finally, multiply the last terms:
(4 - x) (x + 2) = 4 * 2 = 8
Now, combine the like terms obtained from the multiplication:
(4 - x) (x + 2) = 4x - 2x + 4x + 8
Combining the like terms results in:
(4 - x) (x + 2) = 8x + 8
Therefore, option D, -x2 - 2x - 8, is the equivalent expression.