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

Question

Is equality correct?

(x+8)(2x3)=2x2+13x24 (x+8)(2x-3)=2x^2+13x-24

Video Solution

Step-by-Step Solution

To solve this problem, we'll confirm whether (x+8)(2x3)=2x2+13x24(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)(2x3)(x+8)(2x-3).

  • First: Multiply the first terms: x2x=2x2x \cdot 2x = 2x^2.

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

  • Inner: Multiply the inner terms: 82x=16x8 \cdot 2x = 16x.

  • Last: Multiply the last terms: 8(3)=248 \cdot (-3) = -24.

Step 2: Combine these results:

2x2+(3x)+16x+(24)=2x2+13x242x^2 + (-3x) + 16x + (-24) = 2x^2 + 13x - 24

Step 3: Compare with the right-hand side:

The expanded form is 2x2+13x242x^2 + 13x - 24, which matches the right side of the original equation.

Therefore, the expression (x+8)(2x3)(x+8)(2x-3) correctly simplifies to 2x2+13x242x^2 + 13x - 24, verifying the equality.

Thus, the correct answer is: Yes.

Answer

Yes