Question

1 Expandts implify:(X+2)(-x +3X-7 +x)

Answer 1

Given the following expression:

`\mleft(x+2\mright)(-4x^2+3x-9+x^4)`

Let's simplify;

Applying the PEMDAS Rule (Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction).

Step 1: Simplify first the equation within the parenthesis.

`(x+2)(-4x^2+3x-9+x^4)`
`(x+2)\text{ = (x + 2) ; already in simplified form}`
`(-4x^2+3x-9+x^4)\text{ = }(x^4-4x^2+3x-9)\text{ ; already in simplified form}`

Step 2: Proceed with the multiplication.

`(x+2)(x^4-4x^2+3x-9)\text{ }`
`(x)(x^4-4x^2+3x-9)\text{ = }\mleft(x^4\mright)\mleft(x\mright)-(4x^2)(x)+(3x)(x)-(9)(x)=x^5-4x^3+3x^2\text{ - 9x}`
`(2)(x^4-4x^2+3x-9)\text{ = }(x^4)(2)-(4x^2)(2)+(3x)(2)-(9)(2)=2x^4-8x^2+6x-18`

Step 3: Let's add the product of x and 2 being multiplied to -4x^2+3x-9+x^4.

`(x+2)(x^4-4x^2+3x-9)\text{ }`
`(x)(x^4-4x^2+3x-9)\text{ + }(2)(x^4-4x^2+3x-9)`
`(x^5-4x^3+3x^2\text{ - 9x) + }(2x^4-8x^2+6x-18)`
`x^5-4x^3+3x^2\text{ - 9x + }2x^4-8x^2+6x-18`
`x^5\text{+ }2x^4-4x^3+3x^2\text{ }-8x^2\text{- 9x }+6x-18`
`x^5\text{+ }2x^4-4x^3-5x^2\text{-3x}-18`

Therefore, the product of (x+2) (-4x^2+3x-9+x^4) is x^5 + 2x^4 -4x^3 -5x^2 -3x - 18.