Variables and Expressions: Practice

Substitute $4$ for $x$, squaring before multiplying, then subtract the two terms.

$2(4)^2 - 3(4) = 2(16) - 12 = 32 - 12 = 20$

The exponent in the first term applies only to the $4$, not to the coefficient $2$.

Substitute, keeping the negative in parentheses so it is squared correctly.

$(3)^2 + (-4)^2 = 9 + 16 = 25$

A negative squared is positive, since $(-4)(-4) = 16$.

The sum of $x$ and $1$ is $x + 1$, and squaring that whole sum needs parentheses.

$(x + 1)^2$

Without the parentheses, $x^2 + 1$ would square only the $x$.

The expression $4ab$ means $4 \times a \times b$. Substitute both values.

$4(3)(2) = 12 \times 2 = 24$

All three factors multiply together, giving $24$.

Substitute $5$, square first, then handle each term in order.

$(5)^2 - 2(5) + 1 = 25 - 10 + 1 = 16$

Working left to right after the powers and products gives $16$.

Substitute $4$, work inside the parentheses, then multiply.

$3(2 \cdot 4 - 1) = 3(8 - 1) = 3(7) = 21$

The inner expression resolves to $7$ before multiplying by $3$.

The coefficient is the number multiplying that power of the variable.

$5x^2 = 5 \times x^2$

So the coefficient of the $x^2$ term is $5$.

The product is $3n$, four less is $3n - 4$, and "all divided by $2$" puts that whole expression over $2$.

$\frac{3n - 4}{2}$

The word "all" means the entire numerator is divided by $2$.

Substitute $6$, multiply by the decimal coefficient, then add.

$0.5(6) + 1.5 = 3 + 1.5 = 4.5$

So the value is $4.5$.

Substitute $4$ into each factor, evaluate each parenthesis, then multiply.

$(4 - 1)(4 + 2) = (3)(6) = 18$

Each grouped piece is found first, then the two are multiplied.

Substitute $2$ everywhere $x$ appears, work the top, then divide.

$\frac{2(2) + 4}{(2)} = \frac{4 + 4}{2} = \frac{8}{2} = 4$

The same value $2$ replaces both copies of $x$.

Substitute all three values, squaring and multiplying before subtracting.

$(5)^2 - 4(1)(6) = 25 - 24 = 1$

The term $4ac$ is $4 \times 1 \times 6 = 24$, subtracted from $25$.