Questions: If (a=-1) and (b=-2), evaluate: [ a-bleft[(a-b)^2-(a+b)right] ]

Transcript text: 14) If $a=-1$ and $b=-2$, evaluate: \[ a-b\left[(a-b)^{2}-(a+b)\right] \]

Solution

Solution Steps

To evaluate the given expression with the values $ a = -1 $ and $ b = -2 $, we will substitute these values into the expression. Then, we will perform the arithmetic operations following the order of operations: parentheses, exponents, multiplication, and addition/subtraction.

Step 1: Substitute the Given Values

Substitute $ a = -1 $ and $ b = -2 $ into the expression: \[ a - b \left[ (a-b)^2 - (a+b) \right] \] This becomes: \[ -1 - (-2) \left[ (-1 - (-2))^2 - (-1 + (-2)) \right] \]

Step 2: Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: \[ (-1 - (-2)) = (-1 + 2) = 1 \] \[ (-1 + (-2)) = (-1 - 2) = -3 \]

Step 3: Evaluate the Squared Term

Calculate the square of the simplified term: \[ (1)^2 = 1 \]

Step 4: Simplify the Expression

Substitute back into the expression: \[ -1 - (-2) \left[ 1 - (-3) \right] \] Simplify inside the brackets: \[ 1 - (-3) = 1 + 3 = 4 \]

Step 5: Evaluate the Multiplication

Calculate the multiplication: \[ -2 \times 4 = -8 \]

Step 6: Final Calculation

Substitute back into the expression: \[ -1 - (-8) = -1 + 8 = 7 \]