Question

multiplying a binomial by a binomial

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?

\\(\quadx^2 + \quadx + \quad\\)

Explanation:

Expand the distributed terms

$$ (3x)(-x) + (3x)(4) + (-5)(-x) + (-5)(4) = -3x^2 + 12x + 5x - 20 $$

Combine like terms

$$ -3x^2 + (12 + 5)x - 20 = -3x^2 + 17x - 20 $$

Answer:

What is the simplified product in standard form?
<blank>\(-3\)</blank>\(x^2 +\) <blank>\(17\)</blank>\(x +\) <blank>\(-20\)</blank>