Solve 6(x-3)^2+37(x-3)-35

$$6 ( x - 3 ) ^ { 2 } + 37 ( x - 3 ) - 35$$

Evaluate

$$\left(6x-23\right)\left(x+4\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$6\left(x^{2}-6x+9\right)+37\left(x-3\right)-35$$

Use the distributive property to multiply 6 by x^{2}-6x+9.

$$6x^{2}-36x+54+37\left(x-3\right)-35$$

Use the distributive property to multiply 37 by x-3.

$$6x^{2}-36x+54+37x-111-35$$

Combine -36x and 37x to get x.

$$6x^{2}+x+54-111-35$$

Subtract 111 from 54 to get -57.

$$6x^{2}+x-57-35$$

Subtract 35 from -57 to get -92.

$$6x^{2}+x-92$$

Expand

$$6x^{2}+x-92$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$6\left(x^{2}-6x+9\right)+37\left(x-3\right)-35$$

Use the distributive property to multiply 6 by x^{2}-6x+9.

$$6x^{2}-36x+54+37\left(x-3\right)-35$$

Use the distributive property to multiply 37 by x-3.

$$6x^{2}-36x+54+37x-111-35$$

Combine -36x and 37x to get x.

$$6x^{2}+x+54-111-35$$

Subtract 111 from 54 to get -57.

$$6x^{2}+x-57-35$$

Subtract 35 from -57 to get -92.

$$6x^{2}+x-92$$