Question

Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. Use the drop-down menus to identify the steps Lorne used to find the difference. 1. (–3x3 + 5x2 + 4x – 7) + (–6x3 + 2x – 3) 2. (–3x3) + 5x2 + 4x + (–7) + (–6x3) + 2x + (–3) 3. [(–3x3) + (–6x3)] + [4x + 2x] + [(–7) + (–3)] + [5x2] 4. –9x3 + 6x + (–10) + 5x2 5. –9x3 + 5x2 + 6x – 10

Answer 1

Simplify the following:
-(6 x^3 - 2 x + 3) - 3 x^3 + 5 x^2 + 4 x - 7

-(6 x^3 - 2 x + 3) = -6 x^3 + 2 x - 3:
-6 x^3 + 2 x - 3 - 3 x^3 + 5 x^2 + 4 x - 7

Grouping like terms, -3 x^3 - 6 x^3 + 5 x^2 + 4 x + 2 x - 7 - 3 = (-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3):
(-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3)

-3 x^3 - 6 x^3 = -9 x^3:
-9 x^3 + 5 x^2 + (4 x + 2 x) + (-7 - 3)

4 x + 2 x = 6 x:
-9 x^3 + 5 x^2 + 6 x + (-7 - 3)

-7 - 3 = -10:
-9 x^3 + 5 x^2 + 6 x + -10

Factor -1 out of -9 x^3 + 5 x^2 + 6 x - 10:
Answer: -(9 x^3 - 5 x^2 - 6 x + 10)

Answer 2

Answer with Step-by-step explanation:

We have to subtract
`6x^3-2x+3\ from\ -3x^3+5x^2+4x-7`

1.
`(-3x^3+5x^2+4x-7)-(6x^3-2x+3)`

2. Distributing the minus sign in the second bracket and separating all the terms

`(-3x^3) + 5x^2 + 4x + (-7) + (-6x^3) + 2x + (-3)`

3. Combining the like terms

`[(-3x^3) + (-6x^3)] + [4x + 2x] + [(-7) + (-3)] + [5x^2]`

4. Adding the terms with same powers of x

`-9x^3 + 6x + (-10) + 5x^2`

5. Writing the terms in the decreasing powers of x

`-9x^3 + 5x^2 + 6x - 10`