Solve (x^2-7x+6)^2+10(x^2-7x+6)+24

$$( x ^ { 2 } - 7 x + 6 ) ^ { 2 } + 10 ( x ^ { 2 } - 7 x + 6 ) + 24$$

Evaluate

$$\left(x-5\right)\left(x-4\right)\left(x-3\right)\left(x-2\right)$$

Solution Steps

Square x^{2}-7x+6.

$$x^{4}-14x^{3}+61x^{2}-84x+36+10\left(x^{2}-7x+6\right)+24$$

Use the distributive property to multiply 10 by x^{2}-7x+6.

$$x^{4}-14x^{3}+61x^{2}-84x+36+10x^{2}-70x+60+24$$

Combine 61x^{2} and 10x^{2} to get 71x^{2}.

$$x^{4}-14x^{3}+71x^{2}-84x+36-70x+60+24$$

Combine -84x and -70x to get -154x.

$$x^{4}-14x^{3}+71x^{2}-154x+36+60+24$$

Add 36 and 60 to get 96.

$$x^{4}-14x^{3}+71x^{2}-154x+96+24$$

Add 96 and 24 to get 120.

$$x^{4}-14x^{3}+71x^{2}-154x+120$$

Expand

$$x^{4}-14x^{3}+71x^{2}-154x+120$$

Solution Steps

Square x^{2}-7x+6.

$$x^{4}-14x^{3}+61x^{2}-84x+36+10\left(x^{2}-7x+6\right)+24$$

Use the distributive property to multiply 10 by x^{2}-7x+6.

$$x^{4}-14x^{3}+61x^{2}-84x+36+10x^{2}-70x+60+24$$

Combine 61x^{2} and 10x^{2} to get 71x^{2}.

$$x^{4}-14x^{3}+71x^{2}-84x+36-70x+60+24$$

Combine -84x and -70x to get -154x.

$$x^{4}-14x^{3}+71x^{2}-154x+36+60+24$$

Add 36 and 60 to get 96.

$$x^{4}-14x^{3}+71x^{2}-154x+96+24$$

Add 96 and 24 to get 120.

$$x^{4}-14x^{3}+71x^{2}-154x+120$$