Question

simplify the expression below.

(4x(3x - 7) - 19x^2)

(\bigcirc) (-7x^2 - 7)

(\bigcirc) (-7x^2 - 28x)

(\bigcirc) (-31x^2 - 28x)

(\bigcirc) (-35x^2)

Explanation:

Apply the distributive property

We begin by distributing the term \(4x\) to both terms inside the parentheses:

$$ 4x(3x - 7) = (4x \cdot 3x) + (4x \cdot -7) $$

Multiplying the coefficients and variables gives:

$$ 12x^2 - 28x $$

Combine like terms

Now, we substitute this back into the original expression and combine the quadratic terms:

$$ (12x^2 - 28x) - 19x^2 $$

Grouping the \(x^2\) terms together:

$$ (12x^2 - 19x^2) - 28x $$

Subtracting the coefficients:

$$ -7x^2 - 28x $$

Answer:

• (A) \(-7x^2 - 7\)
• (B) \(-7x^2 - 28x\) (Correct answer)
• (C) \(-31x^2 - 28x\)
• (D) \(-35x^2\)