Solve [(-3x)^5:(3x)^4]^2-(6x-y)-[(3x)^2-(2x+3y)]+(8y-5x)

$$[ ( - 3 x ) ^ { 5 } : ( 3 x ) ^ { 4 } ] ^ { 2 } - ( 6 x - y ) - [ ( 3 x ) ^ { 2 } - ( 2 x + 3 y ) ] + ( 8 y - 5 x )$$

Evaluate

$$12y-9x$$

Solution Steps

Expand \left(-3x\right)^{5}.

$$\left(\frac{\left(-3\right)^{5}x^{5}}{\left(3x\right)^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate -3 to the power of 5 and get -243.

$$\left(\frac{-243x^{5}}{\left(3x\right)^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Expand \left(3x\right)^{4}.

$$\left(\frac{-243x^{5}}{3^{4}x^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate 3 to the power of 4 and get 81.

$$\left(\frac{-243x^{5}}{81x^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Cancel out 81x^{4} in both numerator and denominator.

$$\left(-3x\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Expand \left(-3x\right)^{2}.

$$\left(-3\right)^{2}x^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate -3 to the power of 2 and get 9.

$$9x^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

To find the opposite of 6x-y, find the opposite of each term.

$$9x^{2}-6x+y-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Expand \left(3x\right)^{2}.

$$9x^{2}-6x+y-\left(3^{2}x^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-6x+y-\left(9x^{2}-\left(2x+3y\right)\right)+8y-5x$$

To find the opposite of 2x+3y, find the opposite of each term.

$$9x^{2}-6x+y-\left(9x^{2}-2x-3y\right)+8y-5x$$

To find the opposite of 9x^{2}-2x-3y, find the opposite of each term.

$$9x^{2}-6x+y-9x^{2}+2x+3y+8y-5x$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-6x+y+2x+3y+8y-5x$$

Combine -6x and 2x to get -4x.

$$-4x+y+3y+8y-5x$$

Combine y and 3y to get 4y.

$$-4x+4y+8y-5x$$

Combine 4y and 8y to get 12y.

$$-4x+12y-5x$$

Combine -4x and -5x to get -9x.

$$-9x+12y$$

Expand

$$12y-9x$$

Solution Steps

Expand \left(-3x\right)^{5}.

$$\left(\frac{\left(-3\right)^{5}x^{5}}{\left(3x\right)^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate -3 to the power of 5 and get -243.

$$\left(\frac{-243x^{5}}{\left(3x\right)^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Expand \left(3x\right)^{4}.

$$\left(\frac{-243x^{5}}{3^{4}x^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate 3 to the power of 4 and get 81.

$$\left(\frac{-243x^{5}}{81x^{4}}\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Cancel out 81x^{4} in both numerator and denominator.

$$\left(-3x\right)^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Expand \left(-3x\right)^{2}.

$$\left(-3\right)^{2}x^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate -3 to the power of 2 and get 9.

$$9x^{2}-\left(6x-y\right)-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

To find the opposite of 6x-y, find the opposite of each term.

$$9x^{2}-6x+y-\left(\left(3x\right)^{2}-\left(2x+3y\right)\right)+8y-5x$$

Expand \left(3x\right)^{2}.

$$9x^{2}-6x+y-\left(3^{2}x^{2}-\left(2x+3y\right)\right)+8y-5x$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-6x+y-\left(9x^{2}-\left(2x+3y\right)\right)+8y-5x$$

To find the opposite of 2x+3y, find the opposite of each term.

$$9x^{2}-6x+y-\left(9x^{2}-2x-3y\right)+8y-5x$$

To find the opposite of 9x^{2}-2x-3y, find the opposite of each term.

$$9x^{2}-6x+y-9x^{2}+2x+3y+8y-5x$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-6x+y+2x+3y+8y-5x$$

Combine -6x and 2x to get -4x.

$$-4x+y+3y+8y-5x$$

Combine y and 3y to get 4y.

$$-4x+4y+8y-5x$$

Combine 4y and 8y to get 12y.

$$-4x+12y-5x$$

Combine -4x and -5x to get -9x.

$$-9x+12y$$