Question

(-w^3+8w^2-3w)-(4w^2+5w-7)

Answer 1

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Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

`\boxed{-w^3 + 4w^2 + -8w + 7}`

Let's simplify step-by-step.

`(-w^3+8w^2-3w)-(4w^2+5w-7)`

Distribute the Negative Sign:

`= -w^3 + 8w^2 - 3w + -1( 4w^2 + 5w - 7 ) \\= - w^3 + 8w^2 + 3w + -1(4w^2) + -1 (5w)+(-1 )(-7)\\= -w^3 + 8w^2 + -3w + -4w^2 + 5w + 7`

Combine Like Terms:

`= -w^3 + 8w^2 + -3w + -4w^2 + -5w + 7 \\= (-w^3) + ( 8w^3 + -3w + -4w^2) + ( -3w + -5w) + 7 \\= -w^3 + 4w^2 + -8w + 7`

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer 2

`\boxed{ \bold{ { \boxed{ \sf{ - {w}^(3) + 4 {w}^(2) - 8w + 7}}}}}`

Explanation:

`\sf{( - {w}^(3) + 8 {w}^(2) - 3w) - (4 {w}^(2) + 5w - 7)}`

Remove the unnecessary Parentheses

⇒
`\sf{ - {w}^(3) + 8 {w}^(2) - 3w - (4 {w}^(2) + 5w - 7)}`

When there is a ( - ) in front of a parentheses, change the signs of each term in the expression

⇒
`\sf{ - {w}^(3) + 8 {w}^(2) - 3w - 4 {w}^(2) - 5w + 7}`

Collect like terms

⇒
`\sf{ - {w}^(3) + 8 {w}^(2) - 4 {w}^(2) - 3w - 5w + 7}`

⇒
`\sf{ - {w}^(3 ) + 4 {w}^(2) - 8w + 7 }`

Hope I helped!

Best regards!!