Verify the Equation: (-2a+3b)(4c+5a) = 8ac+10a²-12bc-15ab

Is equality correct?

$(-2a+3b)(4c+5a)\stackrel{?}{=}8ac+10a^2-12bc-15ab$

To determine if the given algebraic expression is correct, we will expand the left-hand side using the distributive property:

The expression is $(-2a + 3b)(4c + 5a)$.

Step-by-step expansion:

• Multiply $-2a$ by $4c$: $-2a \times 4c = -8ac$.
• Multiply $-2a$ by $5a$: $-2a \times 5a = -10a^2$.
• Multiply $3b$ by $4c$: $3b \times 4c = 12bc$.
• Multiply $3b$ by $5a$: $3b \times 5a = 15ab$.

Combine these results: $-8ac - 10a^2 + 12bc + 15ab$.

Now compare this result with the right-hand side of the given expression $8ac + 10a^2 - 12bc - 15ab$.

We can observe that each corresponding term has the opposite sign.

This shows that the original statement is incorrect.

Therefore, the expression is actually the negative of what was given, so:

The expression is exactly the same as $-(8ac + 10a^2 - 12bc - 15ab)$.

Thus, the correct choice is:

No, the expression is exactly the same as $-(8ac + 10a^2 - 12bc - 15ab)$.