Solve 5(w-3)^2-(w-3)-(w-3)(5(w-3))

$$5 ( w - 3 ) ^ { 2 } - ( w - 3 ) - ( w - 3 ) ( 5 ( w - 3 ) )$$

Evaluate

$$3-w$$

Solution Steps

Multiply w-3 and w-3 to get \left(w-3\right)^{2}.

$$5\left(w-3\right)^{2}-\left(w-3\right)-\left(w-3\right)^{2}\times 5$$

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

$$5\left(w^{2}-6w+9\right)-\left(w-3\right)-\left(w-3\right)^{2}\times 5$$

Use the distributive property to multiply 5 by w^{2}-6w+9.

$$5w^{2}-30w+45-\left(w-3\right)-\left(w-3\right)^{2}\times 5$$

To find the opposite of w-3, find the opposite of each term.

$$5w^{2}-30w+45-w+3-\left(w-3\right)^{2}\times 5$$

Combine -30w and -w to get -31w.

$$5w^{2}-31w+45+3-\left(w-3\right)^{2}\times 5$$

Add 45 and 3 to get 48.

$$5w^{2}-31w+48-\left(w-3\right)^{2}\times 5$$

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

$$5w^{2}-31w+48-\left(w^{2}-6w+9\right)\times 5$$

Use the distributive property to multiply w^{2}-6w+9 by 5.

$$5w^{2}-31w+48-\left(5w^{2}-30w+45\right)$$

To find the opposite of 5w^{2}-30w+45, find the opposite of each term.

$$5w^{2}-31w+48-5w^{2}+30w-45$$

Combine 5w^{2} and -5w^{2} to get 0.

$$-31w+48+30w-45$$

Combine -31w and 30w to get -w.

$$-w+48-45$$

Subtract 45 from 48 to get 3.

$$-w+3$$

Expand

$$3-w$$

Solution Steps

Multiply w-3 and w-3 to get \left(w-3\right)^{2}.

$$5\left(w-3\right)^{2}-\left(w-3\right)-\left(w-3\right)^{2}\times 5$$

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

$$5\left(w^{2}-6w+9\right)-\left(w-3\right)-\left(w-3\right)^{2}\times 5$$

Use the distributive property to multiply 5 by w^{2}-6w+9.

$$5w^{2}-30w+45-\left(w-3\right)-\left(w-3\right)^{2}\times 5$$

To find the opposite of w-3, find the opposite of each term.

$$5w^{2}-30w+45-w+3-\left(w-3\right)^{2}\times 5$$

Combine -30w and -w to get -31w.

$$5w^{2}-31w+45+3-\left(w-3\right)^{2}\times 5$$

Add 45 and 3 to get 48.

$$5w^{2}-31w+48-\left(w-3\right)^{2}\times 5$$

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

$$5w^{2}-31w+48-\left(w^{2}-6w+9\right)\times 5$$

Use the distributive property to multiply w^{2}-6w+9 by 5.

$$5w^{2}-31w+48-\left(5w^{2}-30w+45\right)$$

To find the opposite of 5w^{2}-30w+45, find the opposite of each term.

$$5w^{2}-31w+48-5w^{2}+30w-45$$

Combine 5w^{2} and -5w^{2} to get 0.

$$-31w+48+30w-45$$

Combine -31w and 30w to get -w.

$$-w+48-45$$

Subtract 45 from 48 to get 3.

$$-w+3$$