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

Question

Fill in the missing values:

(??)(8y7)=8xy32y7x+28 (?-?)(8y-7)=8xy-32y-7x+28

Video Solution

Step-by-Step Solution

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: (x4)(8y7)(x-4)(8y-7).

  • We begin by expanding the left-hand side using the distributive property:
    (x4)(8y7)=x(8y7)4(8y7)(x-4)(8y-7) = x(8y-7) - 4(8y-7).
  • Further expand each component:
    x(8y7)=8xy7xx(8y-7) = 8xy - 7x and 4(8y7)=32y+28-4(8y-7) = -32y + 28.
  • Combine to form:
    8xy7x32y+288xy - 7x - 32y + 28.

We compare this with the right-hand side of the original equation, 8xy32y7x+288xy - 32y - 7x + 28.

The expressions match perfectly upon comparative structuring.

Hence, the missing expression in (x4)(x-4) confirms accurate factorization.

Thus, the missing values that satisfy the equation are x4x-4.

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

Answer

(4,x) (-4,x) x,4 x,-4