Solve (6x+3)(6x+7)-(7x-4)(x-2)

$$(6x+3)(6x+7)-(7x-4)(x-2)$$

Evaluate

$$29x^{2}+78x+13$$

Solution Steps

Apply the distributive property by multiplying each term of 6x+3 by each term of 6x+7.

$$36x^{2}+42x+18x+21-\left(7x-4\right)\left(x-2\right)$$

Combine 42x and 18x to get 60x.

$$36x^{2}+60x+21-\left(7x-4\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 7x-4 by each term of x-2.

$$36x^{2}+60x+21-\left(7x^{2}-14x-4x+8\right)$$

Combine -14x and -4x to get -18x.

$$36x^{2}+60x+21-\left(7x^{2}-18x+8\right)$$

To find the opposite of 7x^{2}-18x+8, find the opposite of each term.

$$36x^{2}+60x+21-7x^{2}-\left(-18x\right)-8$$

The opposite of -18x is 18x.

$$36x^{2}+60x+21-7x^{2}+18x-8$$

Combine 36x^{2} and -7x^{2} to get 29x^{2}.

$$29x^{2}+60x+21+18x-8$$

Combine 60x and 18x to get 78x.

$$29x^{2}+78x+21-8$$

Subtract 8 from 21 to get 13.

$$29x^{2}+78x+13$$

Expand

$$29x^{2}+78x+13$$

Solution Steps

Apply the distributive property by multiplying each term of 6x+3 by each term of 6x+7.

$$36x^{2}+42x+18x+21-\left(7x-4\right)\left(x-2\right)$$

Combine 42x and 18x to get 60x.

$$36x^{2}+60x+21-\left(7x-4\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 7x-4 by each term of x-2.

$$36x^{2}+60x+21-\left(7x^{2}-14x-4x+8\right)$$

Combine -14x and -4x to get -18x.

$$36x^{2}+60x+21-\left(7x^{2}-18x+8\right)$$

To find the opposite of 7x^{2}-18x+8, find the opposite of each term.

$$36x^{2}+60x+21-7x^{2}-\left(-18x\right)-8$$

The opposite of -18x is 18x.

$$36x^{2}+60x+21-7x^{2}+18x-8$$

Combine 36x^{2} and -7x^{2} to get 29x^{2}.

$$29x^{2}+60x+21+18x-8$$

Combine 60x and 18x to get 78x.

$$29x^{2}+78x+21-8$$

Subtract 8 from 21 to get 13.

$$29x^{2}+78x+13$$