What is the simplified product of (2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)

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08-10-2018
Mathematics

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What is the simplified product of (2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)

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thejomezchannel thejomezchannel · Answer 1 · 2018-10-08T21:46:34+02:00

(2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)

Simplifying

(2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x2

2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x

2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)

Reorder the terms for easier multiplication:

2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 2 * -2

2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 3 * -2

2x3 + 2x2 + -4x + 3x2 + 3x + -6

Reorder the terms:

-6 + -4x + 3x + 2x2 + 3x2 + 2x3

Combine like terms: -4x + 3x = -1x

-6 + -1x + 2x2 + 3x2 + 2x3

Combine like terms: 2x2 + 3x2 = 5x2

-6 + -1x + 5x2 + 2x3

sakshigupta4990 sakshigupta4990 · Answer 2 · 2022-05-20T12:23:11+02:00

Answer:

The product is,[tex]-6 + -1x + 5x2 + 2x3[/tex]

explanation:

Simplifying

[tex](2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the parentheses (2x)

[tex]2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x2[/tex]

[tex]2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the closing parentheses (2x)

[tex]2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x[/tex]

[tex]2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove all parentheses (2x)

[tex]2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Rearrange the terms to make multiplication easier:

[tex]2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]2 * -2[/tex]

[tex]2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]3 * -2[/tex]

[tex]2x3 + 2x2 + -4x + 3x2 + 3x + -6[/tex]

Reorder the terms:

[tex]-6 + -4x + 3x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: -4x + 3x = -1x

[tex]-6 + -1x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: 2x2 + 3x2 = 5x2

[tex]-6 + -1x + 5x2 + 2x3[/tex]

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