Question

expressions-polynomials-evaluate
(1 point)
evaluate each algebraic expression for the given value(s):
a) $6 + 3(x - 2)^3$, for $x = 5$
answer:

b) $x^2 - 2(x - y)$, for $x = 7$ and $y = 3$
answer:

Explanation:

Part (a)

Step1: Substitute \( x = 5 \) into the expression

Substitute \( x = 5 \) into \( 6 + 3(x - 2)^3 \), we get \( 6 + 3(5 - 2)^3 \).

Step2: Simplify the parentheses

Calculate \( 5 - 2 = 3 \), so the expression becomes \( 6 + 3(3)^3 \).

Step3: Calculate the exponent

Calculate \( 3^3 = 27 \), then the expression is \( 6 + 3\times27 \).

Step4: Multiply

Calculate \( 3\times27 = 81 \), so the expression is \( 6 + 81 \).

Step5: Add

Calculate \( 6 + 81 = 87 \).

Step1: Substitute \( x = 7 \) and \( y = 3 \) into the expression

Substitute \( x = 7 \) and \( y = 3 \) into \( x^2 - 2(x - y) \), we get \( 7^2 - 2(7 - 3) \).

Step2: Simplify the parentheses

Calculate \( 7 - 3 = 4 \), so the expression becomes \( 7^2 - 2\times4 \).

Step3: Calculate the exponent

Calculate \( 7^2 = 49 \), then the expression is \( 49 - 2\times4 \).

Step4: Multiply

Calculate \( 2\times4 = 8 \), so the expression is \( 49 - 8 \).

Step5: Subtract

Calculate \( 49 - 8 = 41 \).

Answer:

\( 87 \)

Part (b)