From first to last, order the steps to prove that expression A is equivalent to expression B.
Expression A: (x+4)(x−2)
Expression B: x2+2x−8
1. Simplify the expression A by distributive property:
(x + 4)(x - 2)
= x(x - 2) + 4(x - 2)
= x^2 - 2x + 4x - 8
= x^2 + 2x - 8
2. Express the simplified form of expression A as expression B:
Therefore, expression A: (x + 4)(x - 2) is equivalent to expression B: x^2 + 2x - 8.
To prove that Expression A is equivalent to Expression B, we need to expand Expression A and simplify it, then compare it with Expression B. Here are the steps:
Step 1: Expand Expression A using the distributive property:
(x+4)(x-2) = x(x) + x(-2) + 4(x) + 4(-2)
Step 2: Simplify the expanded expression:
x(x) + x(-2) + 4(x) + 4(-2) = x^2 - 2x + 4x - 8
Step 3: Combine like terms:
x^2 - 2x + 4x - 8 = x^2 + 2x - 8
Step 4: Compare the simplified expression with Expression B:
Expression A: (x+4)(x-2) = x^2 + 2x - 8
Expression B: x^2 + 2x - 8
Therefore, Expression A is equivalent to Expression B.