Solve 9(2x+1)^2-42(2x+1)+49

$$9 ( 2 x + 1 ) ^ { 2 } - 42 ( 2 x + 1 ) + 49$$

Evaluate

$$4\left(3x-2\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$9\left(4x^{2}+4x+1\right)-42\left(2x+1\right)+49$$

Use the distributive property to multiply 9 by 4x^{2}+4x+1.

$$36x^{2}+36x+9-42\left(2x+1\right)+49$$

Use the distributive property to multiply -42 by 2x+1.

$$36x^{2}+36x+9-84x-42+49$$

Combine 36x and -84x to get -48x.

$$36x^{2}-48x+9-42+49$$

Subtract 42 from 9 to get -33.

$$36x^{2}-48x-33+49$$

Add -33 and 49 to get 16.

$$36x^{2}-48x+16$$

Expand

$$36x^{2}-48x+16$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$9\left(4x^{2}+4x+1\right)-42\left(2x+1\right)+49$$

Use the distributive property to multiply 9 by 4x^{2}+4x+1.

$$36x^{2}+36x+9-42\left(2x+1\right)+49$$

Use the distributive property to multiply -42 by 2x+1.

$$36x^{2}+36x+9-84x-42+49$$

Combine 36x and -84x to get -48x.

$$36x^{2}-48x+9-42+49$$

Subtract 42 from 9 to get -33.

$$36x^{2}-48x-33+49$$

Add -33 and 49 to get 16.

$$36x^{2}-48x+16$$