Question

Help I need an answer

Write the expression with fewer terms.
3(x−2)+4(x−2)−5(x−2)3(x−2)+4(x−2)−5(x−2)

Answer 1

`-15x^(2) +66x-72`

Explanation:

Simplify or expand:

`3(x-2)+4(x-2)-5(x-2)` ×
`3(x-2)+4(x-2)-5(x-2)`

Multiply the monomials:

3(x-2)+4(x-2)-15(x-2)(x-2)+4(x-2)-5(x-2)

Apply the Distributive Property:

3x-3×2+4(x-2)-15(x-2)(x-2)+4(x-2)-5(x-2)

3x-3×2+4x-4×2-15(x-2)(x-2)+4(x-2)-5(x-2)

3x-3×2+4x-4×2+(-15x-15×(-2))(x-2)+4(x-2)-5(x-2)

3x-3×2+4x-4×2+(-15x-15×(-2))(x-2)+4x-4×2-5(x-2)

3x-3×2+4x-4×2+(-15x-15×(-2))(x-2)+4x-4×2-5x-5×(-2)

Determine the sign for multiplication or division:

3x-3×22+4x-4×2+(-15x+15×2)(x-2)+4x-4×2-5x-5×(-2)

3x-3×2+4x-4×2+(-15x+15×2)(x-2)+4x-4×2-5x+5×2

Calculate the product or quotient:

3x-6+4x-4×2+(-15x+15×2)(x-2)+4x-4×2-5x+5×2

3x-6+4x-8+(-15x+15×2)(x-2)+4x-4×2-5x+5×2

3x-6+4x-8+(-15x+30)(x-2)+4x-4×2-5x+5×2

3x-6+4x-8+(-15x+30)(x-2)+4x-8-5x+5×2

3x-6+4x-8+(-15x+30)(x-2)+4x-8-5x+10

Apply the Distributive Property

3x-6+4x-8-15x(x-2)+30(x-2)+4x-8-5x+10

3x-6+4x-8-15x×x-15x×(-2)+30(x-2)+4x-8

3x-6+4x-8-15x×x-15x×(-2)+30x-30×2+4x-8-5x+10

Determine the sign for multiplication or division:

3x-6+4x-8-15x×x+15x×2+30x-30×2+4x-8-5x+10

Multiply the monomials:

3x-6+4x-8-
`15x^(2)`+15x×2+30x-30×2+4x-8-5x+10

3x-6+4x-8-
`15x^(2)`+30x+30x-30×2+4x-8-5x+10

Calculate the product or quotient:

3x-6+4x-8-
`15x^(2)`+30x+30x-60+4x-8-5x+10

Reorder and gather like terms:

(3x+4x+30x+30x+4x-5x)×x+(-6-8-60-8+10)
`-15x^(2)`

Collect coefficients of like terms:

(3+4+30+30+4-5)×x+(-6-8-60-8+10)
`-15x^(2)`

Calculate the sum or difference:

(7+30+30+4-5)×x+(-6-8-60-8+10)
`-15x^(2)`

(37+30+4-5)×x+(-6-8-60-8+10)
`-15x^(2)`

(67+4-5)×x+(-6-8-60-8+10)
`-15x^(2)`

(71-5)×x+(-6-8-60-8+10)
`-15x^(2)`

66x+(-6-8-60-8+10)
`-15x^(2)`

66x+(-14-60-8+10)
`-15x^(2)`

66x+(-74-8+10)
`-15x^(2)`

66x+(-82+10)
`-15x^(2)`

66x-72
`-15x^(2)`

Rewrite the expression:

`-15x^(2)`+66x-72