Verify the Equality: (2x-3)(-4+y) = -8x+2xy-3y+12

Is equality correct?

$(2x-3)(-4+y)=-8x+2xy-3y+12$

To solve this problem, we'll perform the distribution as follows:

• Distribute the term $(2x-3)$ across $(-4+y)$.

• Calculate $(2x) \times (-4)$ and $(2x) \times y$.

• Calculate $(-3) \times (-4)$ and $(-3) \times y$.

Let's compute these multiplications:

Let us expand the left side using distribution:
$(2x - 3)(-4 + y)$
= $(2x)(-4) + (2x)(y) + (-3)(-4) + (-3)(y)$
= $-8x + 2xy + 12 - 3y$.

After simplification, the expression becomes:

$-8x + 2xy - 3y + 12$.

Comparing this with the right-hand side of the original equation $-8x + 2xy - 3y + 12$, we observe that both sides are equal.

Therefore, the two sides of the equation are equal, confirming that the given equality is correct.

The final solution is Yes.