Verify the Expansion: (x+8)(2x-3) = 2x²+13x-24

Is equality correct?

$(x+8)(2x-3)=2x^2+13x-24$

To solve this problem, we'll confirm whether $(x+8)(2x-3) = 2x^2+13x-24$ is a true equality by expanding and simplifying the left-hand expression.

Step 1: Use the FOIL method to expand $(x+8)(2x-3)$.

• First: Multiply the first terms: $x \cdot 2x = 2x^2$.

• Outer: Multiply the outer terms: $x \cdot (-3) = -3x$.

• Inner: Multiply the inner terms: $8 \cdot 2x = 16x$.

• Last: Multiply the last terms: $8 \cdot (-3) = -24$.

Step 2: Combine these results:

$2x^2 + (-3x) + 16x + (-24) = 2x^2 + 13x - 24$

Step 3: Compare with the right-hand side:

The expanded form is $2x^2 + 13x - 24$, which matches the right side of the original equation.

Therefore, the expression $(x+8)(2x-3)$ correctly simplifies to $2x^2 + 13x - 24$, verifying the equality.

Thus, the correct answer is: Yes.