Solved on Feb 29, 2024

Find the difference of two polynomial expressions and write the result in standard form. $(7x^4 + 6x^5 - 11x) - (12x + 4x^4 - 2x^5)$

STEP 1

Assumptions
1. We are given two polynomials that we need to subtract.
2. Standard form for a polynomial is writing the terms with descending powers of the variable.

STEP 2

Write down the given expression that we need to simplify.
$\left(7 x^{4}+6 x^{5}-11 x\right)-\left(12 x+4 x^{4}-2 x^{5}\right)$

STEP 3

Distribute the negative sign to the terms inside the second parenthesis.
$= 7 x^{4} + 6 x^{5} - 11 x - (12 x) - (4 x^{4}) + (2 x^{5})$

STEP 4

Combine like terms by adding or subtracting the coefficients of the same powers of $x$ .
$= 6 x^{5} + 2 x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x$

STEP 5

Add the coefficients of $x^{5}$ terms.
$= (6 + 2) x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x$

STEP 6

Add the coefficients of $x^{4}$ terms.
$= 8 x^{5} + (7 - 4) x^{4} - 11 x - 12 x$

STEP 7

Add the coefficients of $x$ terms.
$= 8 x^{5} + 3 x^{4} - (11 + 12) x$

STEP 8

Complete the addition of the coefficients.
$= 8 x^{5} + 3 x^{4} - 23 x$

STEP 9

Write the final result in standard form, which is already achieved since the terms are in descending order of their powers.
$= 8 x^{5} + 3 x^{4} - 23 x$
The difference in standard form is $8 x^{5} + 3 x^{4} - 23 x$ .

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Find the difference of two polynomial expressions and write the result in standard form. $(7x^4 + 6x^5 - 11x) - (12x + 4x^4 - 2x^5)$

STEP 1

Assumptions
1. We are given two polynomials that we need to subtract.
2. Standard form for a polynomial is writing the terms with descending powers of the variable.

STEP 2

Write down the given expression that we need to simplify.
$\left(7 x^{4}+6 x^{5}-11 x\right)-\left(12 x+4 x^{4}-2 x^{5}\right)$

STEP 3

Distribute the negative sign to the terms inside the second parenthesis.
$= 7 x^{4} + 6 x^{5} - 11 x - (12 x) - (4 x^{4}) + (2 x^{5})$

STEP 4

Combine like terms by adding or subtracting the coefficients of the same powers of $x$ .
$= 6 x^{5} + 2 x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x$

STEP 5

Add the coefficients of $x^{5}$ terms.
$= (6 + 2) x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x$

STEP 6

Add the coefficients of $x^{4}$ terms.
$= 8 x^{5} + (7 - 4) x^{4} - 11 x - 12 x$

STEP 7

Add the coefficients of $x$ terms.
$= 8 x^{5} + 3 x^{4} - (11 + 12) x$

STEP 8

Complete the addition of the coefficients.
$= 8 x^{5} + 3 x^{4} - 23 x$

STEP 9

Write the final result in standard form, which is already achieved since the terms are in descending order of their powers.
$= 8 x^{5} + 3 x^{4} - 23 x$
The difference in standard form is $8 x^{5} + 3 x^{4} - 23 x$ .

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Find the difference of two polynomial expressions and write the result in standard form. (7x4+6x5−11x)−(12x+4x4−2x5)(7x^4 + 6x^5 - 11x) - (12x + 4x^4 - 2x^5)(7x4+6x5−11x)−(12x+4x4−2x5)

STEP 1

Assumptions1. We are given two polynomials that we need to subtract.2. Standard form for a polynomial is writing the terms with descending powers of the variable.

STEP 2

Write down the given expression that we need to simplify.(7x4+6x5−11x)−(12x+4x4−2x5) \left(7 x^{4}+6 x^{5}-11 x\right)-\left(12 x+4 x^{4}-2 x^{5}\right) (7x4+6x5−11x)−(12x+4x4−2x5)

STEP 3

Distribute the negative sign to the terms inside the second parenthesis.=7x4+6x5−11x−(12x)−(4x4)+(2x5) = 7 x^{4} + 6 x^{5} - 11 x - (12 x) - (4 x^{4}) + (2 x^{5}) =7x4+6x5−11x−(12x)−(4x4)+(2x5)

STEP 4

Combine like terms by adding or subtracting the coefficients of the same powers of xxx.=6x5+2x5+7x4−4x4−11x−12x = 6 x^{5} + 2 x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x =6x5+2x5+7x4−4x4−11x−12x

STEP 5

Add the coefficients of x5x^{5}x5 terms.=(6+2)x5+7x4−4x4−11x−12x = (6 + 2) x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x =(6+2)x5+7x4−4x4−11x−12x

STEP 6

Add the coefficients of x4x^{4}x4 terms.=8x5+(7−4)x4−11x−12x = 8 x^{5} + (7 - 4) x^{4} - 11 x - 12 x =8x5+(7−4)x4−11x−12x

STEP 7

Add the coefficients of xxx terms.=8x5+3x4−(11+12)x = 8 x^{5} + 3 x^{4} - (11 + 12) x =8x5+3x4−(11+12)x

STEP 8

Complete the addition of the coefficients.=8x5+3x4−23x = 8 x^{5} + 3 x^{4} - 23 x =8x5+3x4−23x

STEP 9

Write the final result in standard form, which is already achieved since the terms are in descending order of their powers.=8x5+3x4−23x = 8 x^{5} + 3 x^{4} - 23 x =8x5+3x4−23xThe difference in standard form is 8x5+3x4−23x8 x^{5} + 3 x^{4} - 23 x8x5+3x4−23x.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the difference of two polynomial expressions and write the result in standard form. $(7x^4 + 6x^5 - 11x) - (12x + 4x^4 - 2x^5)$

Assumptions
1. We are given two polynomials that we need to subtract.
2. Standard form for a polynomial is writing the terms with descending powers of the variable.

Write down the given expression that we need to simplify.
$\left(7 x^{4}+6 x^{5}-11 x\right)-\left(12 x+4 x^{4}-2 x^{5}\right)$

Distribute the negative sign to the terms inside the second parenthesis.
$= 7 x^{4} + 6 x^{5} - 11 x - (12 x) - (4 x^{4}) + (2 x^{5})$

Combine like terms by adding or subtracting the coefficients of the same powers of $x$ .
$= 6 x^{5} + 2 x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x$

Add the coefficients of $x^{5}$ terms.
$= (6 + 2) x^{5} + 7 x^{4} - 4 x^{4} - 11 x - 12 x$

Add the coefficients of $x^{4}$ terms.
$= 8 x^{5} + (7 - 4) x^{4} - 11 x - 12 x$

Add the coefficients of $x$ terms.
$= 8 x^{5} + 3 x^{4} - (11 + 12) x$

Complete the addition of the coefficients.
$= 8 x^{5} + 3 x^{4} - 23 x$

Write the final result in standard form, which is already achieved since the terms are in descending order of their powers.
$= 8 x^{5} + 3 x^{4} - 23 x$
The difference in standard form is $8 x^{5} + 3 x^{4} - 23 x$ .