Solve 4*(y-1/2x)*(y+1/2x)-9*(y-1/3x)

$$4 \cdot ( y - \frac { 1 } { 2 } x ) \cdot ( y + \frac { 1 } { 2 } x ) - 9 \cdot ( y - \frac { 1 } { 3 } x )$$

Evaluate

$$-x^{2}+3x+4y^{2}-9y$$

Solution Steps

Use the distributive property to multiply 4 by y-\frac{1}{2}x.

$$\left(4y+4\left(-\frac{1}{2}\right)x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$\left(4y+\frac{4\left(-1\right)}{2}x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Multiply 4 and -1 to get -4.

$$\left(4y+\frac{-4}{2}x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Divide -4 by 2 to get -2.

$$\left(4y-2x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Apply the distributive property by multiplying each term of 4y-2x by each term of y+\frac{1}{2}x.

$$4y^{2}+4y\times \frac{1}{2}x-2xy-2x\times \frac{1}{2}x-9\left(y-\frac{1}{3}x\right)$$

Multiply x and x to get x^{2}.

$$4y^{2}+4y\times \frac{1}{2}x-2xy-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Multiply 4 and \frac{1}{2} to get \frac{4}{2}.

$$4y^{2}+\frac{4}{2}yx-2xy-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Divide 4 by 2 to get 2.

$$4y^{2}+2yx-2xy-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Combine 2yx and -2xy to get 0.

$$4y^{2}-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Multiply -2 times \frac{1}{2}.

$$4y^{2}-x^{2}-9\left(y-\frac{1}{3}x\right)$$

Use the distributive property to multiply -9 by y-\frac{1}{3}x.

$$4y^{2}-x^{2}-9y-9\left(-\frac{1}{3}\right)x$$

Express -9\left(-\frac{1}{3}\right) as a single fraction.

$$4y^{2}-x^{2}-9y+\frac{-9\left(-1\right)}{3}x$$

Multiply -9 and -1 to get 9.

$$4y^{2}-x^{2}-9y+\frac{9}{3}x$$

Divide 9 by 3 to get 3.

$$4y^{2}-x^{2}-9y+3x$$

Expand

$$-x^{2}+3x+4y^{2}-9y$$

Solution Steps

Use the distributive property to multiply 4 by y-\frac{1}{2}x.

$$\left(4y+4\left(-\frac{1}{2}\right)x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$\left(4y+\frac{4\left(-1\right)}{2}x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Multiply 4 and -1 to get -4.

$$\left(4y+\frac{-4}{2}x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Divide -4 by 2 to get -2.

$$\left(4y-2x\right)\left(y+\frac{1}{2}x\right)-9\left(y-\frac{1}{3}x\right)$$

Apply the distributive property by multiplying each term of 4y-2x by each term of y+\frac{1}{2}x.

$$4y^{2}+4y\times \frac{1}{2}x-2xy-2x\times \frac{1}{2}x-9\left(y-\frac{1}{3}x\right)$$

Multiply x and x to get x^{2}.

$$4y^{2}+4y\times \frac{1}{2}x-2xy-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Multiply 4 and \frac{1}{2} to get \frac{4}{2}.

$$4y^{2}+\frac{4}{2}yx-2xy-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Divide 4 by 2 to get 2.

$$4y^{2}+2yx-2xy-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Combine 2yx and -2xy to get 0.

$$4y^{2}-2x^{2}\times \frac{1}{2}-9\left(y-\frac{1}{3}x\right)$$

Multiply -2 times \frac{1}{2}.

$$4y^{2}-x^{2}-9\left(y-\frac{1}{3}x\right)$$

Use the distributive property to multiply -9 by y-\frac{1}{3}x.

$$4y^{2}-x^{2}-9y-9\left(-\frac{1}{3}\right)x$$

Express -9\left(-\frac{1}{3}\right) as a single fraction.

$$4y^{2}-x^{2}-9y+\frac{-9\left(-1\right)}{3}x$$

Multiply -9 and -1 to get 9.

$$4y^{2}-x^{2}-9y+\frac{9}{3}x$$

Divide 9 by 3 to get 3.

$$4y^{2}-x^{2}-9y+3x$$