Find Missing Terms in (?-?)(8y-7) = 8xy-32y-7x+28: Polynomial Expansion

Fill in the missing values:

$(?-?)(8y-7)=8xy-32y-7x+28$

To solve this problem, we will expand the left-hand expression and set it equal to the right-hand side.

Let's rewrite the expression: $(x-4)(8y-7)$.

• We begin by expanding the left-hand side using the distributive property:
  $(x-4)(8y-7) = x(8y-7) - 4(8y-7)$.
• Further expand each component:
  $x(8y-7) = 8xy - 7x$ and $-4(8y-7) = -32y + 28$.
• Combine to form:
  $8xy - 7x - 32y + 28$.

We compare this with the right-hand side of the original equation, $8xy - 32y - 7x + 28$.

The expressions match perfectly upon comparative structuring.

Hence, the missing expression in $(x-4)$ confirms accurate factorization.

Thus, the missing values that satisfy the equation are $x-4$.

Therefore, the missing values are $(-4, x)$ or equivalently $x, -4$.