Question

simplify the following expression. classify the resulting polynomial. 4x(x + 1) - (3x - 8)(x + 4) a. quadratic binomial b. quadratic trinomial c. quadratic monomial d. linear binomial

Explanation:

Step1: Expand the first term

$4x(x + 1) = 4x^2 + 4x$

Step2: Expand the second term

$-(3x - 8)(x + 4) = -(3x^2 + 12x - 8x - 32) = -(3x^2 + 4x - 32) = -3x^2 - 4x + 32$

Step3: Combine the two expanded terms

$(4x^2 + 4x) + (-3x^2 - 4x + 32) = x^2 + 32$

Step4: Classify the polynomial

The polynomial $x^2 + 32$ has degree 2 (quadratic) and 2 terms (binomial). So it is a quadratic binomial.

Answer:

A. quadratic binomial