1) 12(x-2)^{2}
2) 12(x-2)(x-2)
Which expressions are equivalent to `12x^{2}-48x+48`?
Select TWO correct answers.
3 answers
how
To find equivalent expressions to 12x^{2}-48x+48, we can first factor out the greatest common factor, which is 12:
12x^{2}-48x+48 = 12(x^{2}-4x+4)
Next, we can factor the quadratic trinomial x^{2}-4x+4:
x^{2}-4x+4 = (x-2)(x-2) = (x-2)^{2}
Therefore, putting it all together, we get:
12(x^{2}-4x+4) = 12(x-2)^{2}
Thus, the expression 12(x-2)^{2} is equivalent to 12x^{2}-48x+48. The other correct answer, 12(x-2)(x-2), is simply another way of writing the same factored form.
12x^{2}-48x+48 = 12(x^{2}-4x+4)
Next, we can factor the quadratic trinomial x^{2}-4x+4:
x^{2}-4x+4 = (x-2)(x-2) = (x-2)^{2}
Therefore, putting it all together, we get:
12(x^{2}-4x+4) = 12(x-2)^{2}
Thus, the expression 12(x-2)^{2} is equivalent to 12x^{2}-48x+48. The other correct answer, 12(x-2)(x-2), is simply another way of writing the same factored form.
1 answer