Solve (2w+3x)(w-5x)-(3w+7x)(w-7x)

$$( 2 w + 3 x ) ( w - 5 x ) - ( 3 w + 7 x ) ( w - 7 x )$$

Evaluate

$$34x^{2}+7wx-w^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2w+3x by each term of w-5x.

$$2w^{2}-10wx+3xw-15x^{2}-\left(3w+7x\right)\left(w-7x\right)$$

Combine -10wx and 3xw to get -7wx.

$$2w^{2}-7wx-15x^{2}-\left(3w+7x\right)\left(w-7x\right)$$

Apply the distributive property by multiplying each term of 3w+7x by each term of w-7x.

$$2w^{2}-7wx-15x^{2}-\left(3w^{2}-21wx+7xw-49x^{2}\right)$$

Combine -21wx and 7xw to get -14wx.

$$2w^{2}-7wx-15x^{2}-\left(3w^{2}-14wx-49x^{2}\right)$$

To find the opposite of 3w^{2}-14wx-49x^{2}, find the opposite of each term.

$$2w^{2}-7wx-15x^{2}-3w^{2}-\left(-14wx\right)-\left(-49x^{2}\right)$$

The opposite of -14wx is 14wx.

$$2w^{2}-7wx-15x^{2}-3w^{2}+14wx-\left(-49x^{2}\right)$$

The opposite of -49x^{2} is 49x^{2}.

$$2w^{2}-7wx-15x^{2}-3w^{2}+14wx+49x^{2}$$

Combine 2w^{2} and -3w^{2} to get -w^{2}.

$$-w^{2}-7wx-15x^{2}+14wx+49x^{2}$$

Combine -7wx and 14wx to get 7wx.

$$-w^{2}+7wx-15x^{2}+49x^{2}$$

Combine -15x^{2} and 49x^{2} to get 34x^{2}.

$$-w^{2}+7wx+34x^{2}$$

Expand

$$34x^{2}+7wx-w^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2w+3x by each term of w-5x.

$$2w^{2}-10wx+3xw-15x^{2}-\left(3w+7x\right)\left(w-7x\right)$$

Combine -10wx and 3xw to get -7wx.

$$2w^{2}-7wx-15x^{2}-\left(3w+7x\right)\left(w-7x\right)$$

Apply the distributive property by multiplying each term of 3w+7x by each term of w-7x.

$$2w^{2}-7wx-15x^{2}-\left(3w^{2}-21wx+7xw-49x^{2}\right)$$

Combine -21wx and 7xw to get -14wx.

$$2w^{2}-7wx-15x^{2}-\left(3w^{2}-14wx-49x^{2}\right)$$

To find the opposite of 3w^{2}-14wx-49x^{2}, find the opposite of each term.

$$2w^{2}-7wx-15x^{2}-3w^{2}-\left(-14wx\right)-\left(-49x^{2}\right)$$

The opposite of -14wx is 14wx.

$$2w^{2}-7wx-15x^{2}-3w^{2}+14wx-\left(-49x^{2}\right)$$

The opposite of -49x^{2} is 49x^{2}.

$$2w^{2}-7wx-15x^{2}-3w^{2}+14wx+49x^{2}$$

Combine 2w^{2} and -3w^{2} to get -w^{2}.

$$-w^{2}-7wx-15x^{2}+14wx+49x^{2}$$

Combine -7wx and 14wx to get 7wx.

$$-w^{2}+7wx-15x^{2}+49x^{2}$$

Combine -15x^{2} and 49x^{2} to get 34x^{2}.

$$-w^{2}+7wx+34x^{2}$$