Solve 2(2x-5y)(3x+4y)-6(2x-5y)(x-y)

$$2 ( 2 x - 5 y ) ( 3 x + 4 y ) - 6 ( 2 x - 5 y ) ( x - y )$$

Evaluate

$$14y\left(2x-5y\right)$$

Solution Steps

Use the distributive property to multiply 2 by 2x-5y.

$$\left(4x-10y\right)\left(3x+4y\right)-6\left(2x-5y\right)\left(x-y\right)$$

Apply the distributive property by multiplying each term of 4x-10y by each term of 3x+4y.

$$12x^{2}+16xy-30yx-40y^{2}-6\left(2x-5y\right)\left(x-y\right)$$

Combine 16xy and -30yx to get -14xy.

$$12x^{2}-14xy-40y^{2}-6\left(2x-5y\right)\left(x-y\right)$$

Use the distributive property to multiply -6 by 2x-5y.

$$12x^{2}-14xy-40y^{2}+\left(-12x+30y\right)\left(x-y\right)$$

Apply the distributive property by multiplying each term of -12x+30y by each term of x-y.

$$12x^{2}-14xy-40y^{2}-12x^{2}+12xy+30yx-30y^{2}$$

Combine 12xy and 30yx to get 42xy.

$$12x^{2}-14xy-40y^{2}-12x^{2}+42xy-30y^{2}$$

Combine 12x^{2} and -12x^{2} to get 0.

$$-14xy-40y^{2}+42xy-30y^{2}$$

Combine -14xy and 42xy to get 28xy.

$$28xy-40y^{2}-30y^{2}$$

Combine -40y^{2} and -30y^{2} to get -70y^{2}.

$$28xy-70y^{2}$$

Expand

$$28xy-70y^{2}$$

Solution Steps

Use the distributive property to multiply 2 by 2x-5y.

$$\left(4x-10y\right)\left(3x+4y\right)-6\left(2x-5y\right)\left(x-y\right)$$

Apply the distributive property by multiplying each term of 4x-10y by each term of 3x+4y.

$$12x^{2}+16xy-30yx-40y^{2}-6\left(2x-5y\right)\left(x-y\right)$$

Combine 16xy and -30yx to get -14xy.

$$12x^{2}-14xy-40y^{2}-6\left(2x-5y\right)\left(x-y\right)$$

Use the distributive property to multiply -6 by 2x-5y.

$$12x^{2}-14xy-40y^{2}+\left(-12x+30y\right)\left(x-y\right)$$

Apply the distributive property by multiplying each term of -12x+30y by each term of x-y.

$$12x^{2}-14xy-40y^{2}-12x^{2}+12xy+30yx-30y^{2}$$

Combine 12xy and 30yx to get 42xy.

$$12x^{2}-14xy-40y^{2}-12x^{2}+42xy-30y^{2}$$

Combine 12x^{2} and -12x^{2} to get 0.

$$-14xy-40y^{2}+42xy-30y^{2}$$

Combine -14xy and 42xy to get 28xy.

$$28xy-40y^{2}-30y^{2}$$

Combine -40y^{2} and -30y^{2} to get -70y^{2}.

$$28xy-70y^{2}$$