Expanding and Factoring Expressions: Practice

Distribute the $-3$; the product $(-3)(-5) = 15$ is positive.

$-3(2x - 5) = -6x + 15$

Distribute the $2x$; note $2x \cdot 3x = 6x^2$.

$2x(3x - 4) = 6x^2 - 8x$

Multiply every term, then combine the middle products $-2x$ and $5x$.

$(x + 5)(x - 2) = x^2 - 2x + 5x - 10 = x^2 + 3x - 10$

The middle products are $6x$ and $x$, which combine to $7x$.

$(2x + 1)(x + 3) = 2x^2 + 6x + x + 3 = 2x^2 + 7x + 3$

Both middle products are negative, and $(-4)(-3) = 12$.

$(x - 4)(x - 3) = x^2 - 3x - 4x + 12 = x^2 - 7x + 12$

The GCF combines the number $2$ and one $x$, giving $2x$; the partial factorings leave a shared factor inside.

$4x^2 + 6x = 2x(2x + 3)$

The factor $-x$ flips each sign; $(-x)(-6) = 6x$.

$-x(x - 6) = -x^2 + 6x$

Multiply $3x^2$ by each term; $3x^2 \cdot 2x = 6x^3$.

$3x^2(2x - 1) = 6x^3 - 3x^2$

The greatest common factor of $12x$ and $8$ is $4$.

$12x - 8 = 4(3x - 2)$

Distribute the $2$, then combine like terms.

$2(3x - 1) - x = 6x - 2 - x = 5x - 2$

Combine the middle products $-x$ and $4x$.

$(x + 4)(x - 1) = x^2 - x + 4x - 4 = x^2 + 3x - 4$

Distribute the $-2x$; both products come out negative.

$-2x(3x + 5) = -6x^2 - 10x$