Question

multiply and simplify: $(2x + 7)(x - 3) = \boxed{\text{type your answer...}}x^2 + \boxed{\text{type your answer...}}x - \boxed{\text{type your answer...}}$

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
$(2x + 7)(x - 3) = 2x \cdot x + 2x \cdot (-3) + 7 \cdot x + 7 \cdot (-3)$

Step2: Simplify each product

Calculate each term:
$2x \cdot x = 2x^2$,
$2x \cdot (-3) = -6x$,
$7 \cdot x = 7x$,
$7 \cdot (-3) = -21$

Step3: Combine like terms

Combine the linear terms ($-6x + 7x$):
$2x^2 + (-6x + 7x) - 21 = 2x^2 + x - 21$

Answer:

The coefficients are $2$ (for $x^2$), $1$ (for $x$), and $21$ (the constant term). So the filled form is:
$(2x + 7)(x - 3) = \boldsymbol{2}x^2 + \boldsymbol{1}x - \boldsymbol{21}$