Solve 3(4x+1)^2+11(4x+1)-20

$$3 ( 4 x + 1 ) ^ { 2 } + 11 ( 4 x + 1 ) - 20$$

Evaluate

$$48x^{2}+68x-6$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+1\right)^{2}.

$$3\left(16x^{2}+8x+1\right)+11\left(4x+1\right)-20$$

Use the distributive property to multiply 3 by 16x^{2}+8x+1.

$$48x^{2}+24x+3+11\left(4x+1\right)-20$$

Use the distributive property to multiply 11 by 4x+1.

$$48x^{2}+24x+3+44x+11-20$$

Combine 24x and 44x to get 68x.

$$48x^{2}+68x+3+11-20$$

Add 3 and 11 to get 14.

$$48x^{2}+68x+14-20$$

Subtract 20 from 14 to get -6.

$$48x^{2}+68x-6$$

Expand

$$48x^{2}+68x-6$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+1\right)^{2}.

$$3\left(16x^{2}+8x+1\right)+11\left(4x+1\right)-20$$

Use the distributive property to multiply 3 by 16x^{2}+8x+1.

$$48x^{2}+24x+3+11\left(4x+1\right)-20$$

Use the distributive property to multiply 11 by 4x+1.

$$48x^{2}+24x+3+44x+11-20$$

Combine 24x and 44x to get 68x.

$$48x^{2}+68x+3+11-20$$

Add 3 and 11 to get 14.

$$48x^{2}+68x+14-20$$

Subtract 20 from 14 to get -6.

$$48x^{2}+68x-6$$