Solve for M M-(4ab-3b^2)=a^2-7ab+8b^2

$M - (4 a b - 3 b^{2}) = a^{2} - 7 a b + 8 b^{2}$

Step 1

Simplify each term.

Apply the distributive property.

$M - (4 a b) - (- 3 b^{2}) = a^{2} - 7 a b + 8 b^{2}$

Multiply $4$ by $- 1$ .

$M - 4 (a b) - (- 3 b^{2}) = a^{2} - 7 a b + 8 b^{2}$

Multiply $- 3$ by $- 1$ .

$M - 4 a b + 3 b^{2} = a^{2} - 7 a b + 8 b^{2}$

Step 2

Move all terms not containing $M$ to the right side of the equation.

Add $4 a b$ to both sides of the equation.

$M + 3 b^{2} = a^{2} - 7 a b + 8 b^{2} + 4 a b$

Subtract $3 b^{2}$ from both sides of the equation.

$M = a^{2} - 7 a b + 8 b^{2} + 4 a b - 3 b^{2}$

Add $- 7 a b$ and $4 a b$ .

$M = a^{2} + 8 b^{2} - 3 a b - 3 b^{2}$

Subtract $3 b^{2}$ from $8 b^{2}$ .

$M = a^{2} + 5 b^{2} - 3 a b$