Question

Multiply: (3x−5)(−x+4)

Applying the distributive property, the expression becomes (3x)(−x)+(3x)(4)+(−5)(−x)+(−5)(4).

What is the simplified product in standard form?


x2+
x+

Answer 1

-3x^2 + 12x + 5x - 20 = -3x^2 + 17x - 20

Explanation:

(-3x - 5)(-x + 4) is a binomial expression, where (-3x - 5) is one expression and (-x + 4) is the other.

As the text eludes to, we can multiply binomial expressions using the FOIL method, where you multiply the first terms (3x and -x), outer terms (3x and 4), the inner terms (-5 and -x), and the last terms (-5 and 4)

This is how you get

(3x)(-x) + (3x)(4) + (-5)(-x) + (-5)(4)

Now, multiply the terms and combine like terms:

`(3x)(-x)+(3x)(4)+(-5)(-x)+(-5)(4)\\-3x^2+12x+5x-20\\-3x^2+17x-20`