Question

Find the missing term. g ( g 2 − h 2 ) − ? ( g − h ) 2 = g 2 − 2 ⁢ g ⁢ h − h 2 ( g − h ) 2 ⁢ ( g + h ) Replace the question mark (?) with to make the equation true.

Answer 1

gh^2

Explanation:

To find the missing term, we can compare the left side and right side of the equation.

The given equation is:

g(g^2 - h^2) - ?(g - h)^2 = g^2 - 2gh - h^2(g - h)^2(g + h)

Let's expand the terms on both sides of the equation:

Left side:

g(g^2 - h^2) - ?(g - h)^2

= g^3 - gh^2 - ?(g^2 - 2gh + h^2)

Right side:

g^2 - 2gh - h^2(g - h)^2(g + h)

= g^2 - 2gh - h^2(g^2 - 2gh + h^2)(g + h)

Now, let's equate the expanded forms:

g^3 - gh^2 - ?(g^2 - 2gh + h^2) = g^2 - 2gh - h^2(g^2 - 2gh + h^2)(g + h)

Comparing the like terms, we can see that the term with gh^2 is missing on the right side. Therefore, we need to replace the question mark (?) with gh^2 to make the equation true.

So the missing term is gh^2.