Arithmetic with Expressions: Practice

The $x^2$ terms and the $x$ terms are unlike, so combine each kind on its own.

$3x^2 - x^2 = 2x^2, \quad 2x + 5x = 7x$

The result is $2x^2 + 7x$.

A leading minus sign is the factor $-1$ distributed over each term.

$-(3x - 5) = -3x + 5$

The minus sign flips both terms of $(x - 7)$.

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

The term $-x^2$ has an understood coefficient of $-1$.

$-x^2 = -1x^2$

Multiply $-2$ across each term, so $-2 \cdot (-3) = +6$.

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

Like terms need the same variable part, and $x$ differs from $x^2$ in exponent.

$2x \text{ and } 2x^2 \text{ are unlike}$

The other pairs each share a variable part, and $4$ and $9$ are both constants.

Combine the $y$ terms and the constants.

$10y - 4 - 6y - 3 = (10y - 6y) + (-4 - 3) = 4y - 7$

Distribute the $5$, then combine like terms.

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

Expand each choice. Only the first returns $6x + 4$.

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

The others give $6x + 8$, $6x + 24$, and $6x + 12$.

Combine like terms first, then substitute $x = 3$.

$(4x + 1) + (2x - 5) = 6x - 4, \quad 6(3) - 4 = 14$

Distribute the factor $x$ across each term inside.

$x(2x + 3) = x \cdot 2x + x \cdot 3 = 2x^2 + 3x$

Distribute the $2$, then combine like terms.

$2(a + 3) + (a - 3) = 2a + 6 + a - 3 = 3a + 3$