Verify the Expansion: (4x+3)(8x+5) = 32x²+44x+15

Is equality correct?

$(4x+3)(8x+5)=32x^2+44x+15$

To solve this problem, we'll employ the distributive property to verify the given equality:

Step 1: Expand the left-hand side expression $(4x+3)(8x+5)$:

• Calculate $4x \cdot 8x = 32x^2$

• Calculate $4x \cdot 5 = 20x$

• Calculate $3 \cdot 8x = 24x$

• Calculate $3 \cdot 5 = 15$

Step 2: Combine like terms:

The expanded form is:
$32x^2 + 20x + 24x + 15$

Combine like terms $20x$ and $24x$:

This gives us $32x^2 + (20x + 24x) + 15 = 32x^2 + 44x + 15$.

Step 3: Compare the expanded form with the right-hand side expression:

The expanded form, $32x^2 + 44x + 15$, matches the right-hand side exactly.

Thus, the given equality $(4x+3)(8x+5) = 32x^2 + 44x + 15$ is correct.

The correct answer is Yes.