Answer:
B. [tex] (x - 4)^2 [/tex]
Step-by-step explanation:
To determine the equivalent expression of [tex] x^2 - 8x + 16 [/tex], factorise the given expression as follows:
[tex] x^2 - 8x + 16 [/tex]
Look for two numbers that will give you "-8" when added together, and will equally give you "16" when multiplied together.
Thus: -4 + -4 = -8; also, -4 × -4 = 16.
Therefore, -4x and -4x is what we would use to replace "-8x" in the expression as follows:
[tex] x^2 - 4x - 4x + 16 [/tex]
[tex] x(x - 4) -4(x - 4) [/tex]
[tex] (x - 4)(x - 4) [/tex]
[tex] (x - 4)(x - 4) = (x - 4)^2 [/tex]
Therefore, [tex] x^2 - 8x + 16 = (x - 4)^2 [/tex]
