Solve 4ax-{(x+y)(x-5)-[(x+y)(x+5)-2x(a-y)]+2x(a+y-6)}

$$4 a x - \{ ( x + y ) ( x - 5 ) - [ ( x + y ) ( x + 5 ) - 2 x ( a - y ) ] + 2 x ( a + y - 6 ) \}$$

Evaluate

$$22x+10y$$

Solution Steps

Apply the distributive property by multiplying each term of x+y by each term of x-5.

$$4ax-\left(x^{2}-5x+yx-5y-\left(\left(x+y\right)\left(x+5\right)-2x\left(a-y\right)\right)+2x\left(a+y-6\right)\right)$$

Apply the distributive property by multiplying each term of x+y by each term of x+5.

$$4ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)+2x\left(a+y-6\right)\right)$$

Use the distributive property to multiply 2x by a+y-6.

$$4ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)+2xa+2xy-12x\right)$$

To find the opposite of x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)+2xa+2xy-12x, find the opposite of each term.

$$4ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)\right)-2xa-2xy-\left(-12x\right)$$

Combine 4ax and -2xa to get 2ax.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)\right)-2xy-\left(-12x\right)$$

The opposite of -12x is 12x.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)\right)-2xy+12x$$

Use the distributive property to multiply -2x by a-y.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2xa+2xy\right)\right)-2xy+12x$$

Combine yx and 2xy to get 3yx.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+3yx+5y-2xa\right)\right)-2xy+12x$$

To find the opposite of x^{2}+5x+3yx+5y-2xa, find the opposite of each term.

$$2ax-\left(x^{2}-5x+yx-5y-x^{2}-5x-3yx-5y-\left(-2xa\right)\right)-2xy+12x$$

The opposite of -2xa is 2xa.

$$2ax-\left(x^{2}-5x+yx-5y-x^{2}-5x-3yx-5y+2xa\right)-2xy+12x$$

Combine x^{2} and -x^{2} to get 0.

$$2ax-\left(-5x+yx-5y-5x-3yx-5y+2xa\right)-2xy+12x$$

Combine -5x and -5x to get -10x.

$$2ax-\left(-10x+yx-5y-3yx-5y+2xa\right)-2xy+12x$$

Combine yx and -3yx to get -2yx.

$$2ax-\left(-10x-2yx-5y-5y+2xa\right)-2xy+12x$$

Combine -5y and -5y to get -10y.

$$2ax-\left(-10x-2yx-10y+2xa\right)-2xy+12x$$

To find the opposite of -10x-2yx-10y+2xa, find the opposite of each term.

$$2ax-\left(-10x\right)-\left(-2yx\right)-\left(-10y\right)-2xa-2xy+12x$$

The opposite of -10x is 10x.

$$2ax+10x-\left(-2yx\right)-\left(-10y\right)-2xa-2xy+12x$$

The opposite of -2yx is 2yx.

$$2ax+10x+2yx-\left(-10y\right)-2xa-2xy+12x$$

The opposite of -10y is 10y.

$$2ax+10x+2yx+10y-2xa-2xy+12x$$

Combine 2ax and -2xa to get 0.

$$10x+2yx+10y-2xy+12x$$

Combine 2yx and -2xy to get 0.

$$10x+10y+12x$$

Combine 10x and 12x to get 22x.

$$22x+10y$$

Expand

$$22x+10y$$

Solution Steps

Apply the distributive property by multiplying each term of x+y by each term of x-5.

$$4ax-\left(x^{2}-5x+yx-5y-\left(\left(x+y\right)\left(x+5\right)-2x\left(a-y\right)\right)+2x\left(a+y-6\right)\right)$$

Apply the distributive property by multiplying each term of x+y by each term of x+5.

$$4ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)+2x\left(a+y-6\right)\right)$$

Use the distributive property to multiply 2x by a+y-6.

$$4ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)+2xa+2xy-12x\right)$$

To find the opposite of x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)+2xa+2xy-12x, find the opposite of each term.

$$4ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)\right)-2xa-2xy-\left(-12x\right)$$

Combine 4ax and -2xa to get 2ax.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)\right)-2xy-\left(-12x\right)$$

The opposite of -12x is 12x.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2x\left(a-y\right)\right)\right)-2xy+12x$$

Use the distributive property to multiply -2x by a-y.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+yx+5y-2xa+2xy\right)\right)-2xy+12x$$

Combine yx and 2xy to get 3yx.

$$2ax-\left(x^{2}-5x+yx-5y-\left(x^{2}+5x+3yx+5y-2xa\right)\right)-2xy+12x$$

To find the opposite of x^{2}+5x+3yx+5y-2xa, find the opposite of each term.

$$2ax-\left(x^{2}-5x+yx-5y-x^{2}-5x-3yx-5y-\left(-2xa\right)\right)-2xy+12x$$

The opposite of -2xa is 2xa.

$$2ax-\left(x^{2}-5x+yx-5y-x^{2}-5x-3yx-5y+2xa\right)-2xy+12x$$

Combine x^{2} and -x^{2} to get 0.

$$2ax-\left(-5x+yx-5y-5x-3yx-5y+2xa\right)-2xy+12x$$

Combine -5x and -5x to get -10x.

$$2ax-\left(-10x+yx-5y-3yx-5y+2xa\right)-2xy+12x$$

Combine yx and -3yx to get -2yx.

$$2ax-\left(-10x-2yx-5y-5y+2xa\right)-2xy+12x$$

Combine -5y and -5y to get -10y.

$$2ax-\left(-10x-2yx-10y+2xa\right)-2xy+12x$$

To find the opposite of -10x-2yx-10y+2xa, find the opposite of each term.

$$2ax-\left(-10x\right)-\left(-2yx\right)-\left(-10y\right)-2xa-2xy+12x$$

The opposite of -10x is 10x.

$$2ax+10x-\left(-2yx\right)-\left(-10y\right)-2xa-2xy+12x$$

The opposite of -2yx is 2yx.

$$2ax+10x+2yx-\left(-10y\right)-2xa-2xy+12x$$

The opposite of -10y is 10y.

$$2ax+10x+2yx+10y-2xa-2xy+12x$$

Combine 2ax and -2xa to get 0.

$$10x+2yx+10y-2xy+12x$$

Combine 2yx and -2xy to get 0.

$$10x+10y+12x$$

Combine 10x and 12x to get 22x.

$$22x+10y$$