Question

which expression has an equivalent value to $x^2 + 9x + 8$ for all values of $x$?
$(x + 1)(x + 8)$
$(x + 2)(x + 6)$
$(x + 4)(x + 4)$
$(x + 5)(x + 4)$

Explanation:

Step1: Expand option A

$(x+1)(x+8) = x^2 + 8x + x + 8 = x^2 + 9x + 8$

Step2: Verify other options

$(x+2)(x+6) = x^2 + 6x + 2x + 12 = x^2 + 8x + 12$
$(x+4)(x+4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16$
$(x+5)(x+4) = x^2 + 4x + 5x + 20 = x^2 + 9x + 20$

Answer:

A. $(x + 1)(x + 8)$