Question

Which answer choice is equivalent to the expression (x+2)^2 - 6x+2?

a. x^2 - 2x+8x
b. x^2 - 2x+6
c. x^2 - 6x+4
d. -5x^2 +6

Answer 1

(x+2)^2 - 6x+2

(x+2)^2 = (x+2).(x+2)

= x(x+2) + 2(x+2)

= xx + x2 + 2x +4 ( x2 = 2x)

= x^2+ 4x +4

(x+2)^2 - 6x+2

x^2+ 4x +4- 6x+2

x^2+ 4x - 6x+2 +4

x^2- 2x+2 + 6 (b)

Explanation:

Answer 2

The expression (x+2)^2 - 6x+2 is equivalent to x^2 - 2x + 2. therefore, option b is correct

The expression (x+2)^2 - 6x+2 can be simplified by using the FOIL method to expand the squared term. FOIL stands for First, Outer, Inner, Last and is a way to multiply two binomials:

(x+2)(x+2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4

Now we subtract 6x and 2 from this expanded expression:

x^2 + 4x + 4 - 6x - 2 = x^2 - 2x + 2

Therefore, the equivalent expression is x^2 - 2x + 2, so the correct answer is (b) x^2 - 2x + 6.