Question

Write the product (x−8)(x+4) as an equivalent trinomial.

a. x^2-4x-32
b. x^2-4x+32
c. x^2+4x-32
d. x^2+4x+32

Answer 1

To find the equivalent trinomial for the product (x-8)(x+4), we use the FOIL method to expand the binomials, resulting in the trinomial x^2 - 4x - 32, which corresponds to option a.

Step-by-step explanation:

To write the product (x-8)(x+4) as an equivalent trinomial, we can use the FOIL method, which stands for First, Outer, Inner, Last, to multiply the two binomials.

1. Multiply the First terms in each binomial: x * x = x^2.
2. Multiply the Outer terms: x * 4 = 4x.
3. Multiply the Inner terms: (-8) * x = -8x.
4. Multiply the Last terms: (-8) * 4 = -32.
5. Combine the like terms (4x and -8x) to get -4x.
6. The resulting trinomial is x^2 - 4x - 32.

Therefore, the equivalent trinomial is x^2 - 4x - 32, which matches option a.