If x = -3 and y = 2, what is the value of the expression x^2 - y(x - y^3)? — ACT

If $x = -3$ and $y = 2$ , what is the value of the expression $x^2 - y(x - y^3)$ ?

Substituting

x = -3

and

y = 2

into the expression gives

x^2 - y(x - y^3) = (-3)^2 - 2(-3 - 2^3)

. Evaluating exponents first, we get

9 - 2(-3 - 8)

. Simplifying inside the parentheses gives

9 - 2(-11)

. Multiplying before subtracting yields

9 - (-22) = 9 + 22 = 31

Substitute the given values into the expression

(-3)^2 - 2((-3) - 2^3)

To evaluate the expression for the specific numbers

x = -3

and

y = 2

Evaluate the exponents outside and inside the parentheses

9 - 2(-3 - 8)

Exponents must be calculated before multiplication and subtraction, according to PEMDAS rules. Note that

(-3)^2 = 9

and

2^3 = 8

Perform the operations inside the parentheses

9 - 2(-11)

Parentheses have the highest priority in the order of operations.

Multiply the terms

9 - (-22) = 9 + 22

Multiplication must be performed before subtraction.

Perform final addition

Adding 22 to 9 yields the final simplified value.

Order of operations (PEMDAS) and substitution of negative numbers in exponents.

Question