Identify two expressions that will be equivalent to 2x2−8x−10 when distributed. Enter the option with the lesser number first.
-2(x^2 - 4x - 5) or -2(x^2 + 4x + 5)
To find two expressions that will be equivalent to 2x^2 - 8x - 10 when distributed, let's start by factoring out the common factor (if any) from the given expression:
2x^2 - 8x - 10
The greatest common factor (GCF) of all the terms is 2. Factoring out 2, we get:
2(x^2 - 4x - 5)
Now, let's explore two possible ways to distribute the remaining expression:
1. Distributing the expression inside the parentheses without factoring it further:
2(x^2 - 4x - 5) can be distributed as:
2x^2 - 8x - 10
Therefore, one equivalent expression is: 2x^2 - 8x - 10.
2. Factoring the expression inside the parentheses:
The expression x^2 - 4x - 5 cannot be factored further using integers. Hence, we can multiply the leading coefficient by the constant term (-1 * 5) to find two numbers that add up to the middle coefficient (-4). The numbers are -5 and 1. This allows us to factor the expression as follows:
x^2 - 4x - 5 = (x - 5)(x + 1)
Now, let's distribute the expression:
2(x - 5)(x + 1)
= 2(x^2 - 5x + x - 5)
= 2(x^2 - 4x - 5)
Therefore, the other equivalent expression is: 2(x^2 - 4x - 5).
Hence, the two expressions that are equivalent to 2x^2 - 8x - 10 when distributed are:
1. 2x^2 - 8x - 10
2. 2(x^2 - 4x - 5)