Question Subtract $6 z^{2} - 8 z + 2$ and $-(4 z^{2} + 7 z - 4)$ .

Studdy Solution

STEP 1

Assumptions
1. We are given two polynomials: $6z^2 - 8z + 2$ and $4z^2 + 7z - 4$ .
2. We need to subtract the second polynomial from the first one.

STEP 2

Write down the given polynomials, aligning like terms.
$\begin{array}{r} 6z^2 - 8z + 2 \\ -(4z^2 + 7z - 4) \\ \end{array}$

STEP 3

Distribute the negative sign across the second polynomial.
$\begin{array}{r} 6z^2 - 8z + 2 \\ -4z^2 - 7z + 4 \\ \end{array}$

STEP 4

Subtract the coefficients of the like terms.
For the $z^2$ terms: $6z^2 - 4z^2 = (6 - 4)z^2 = 2z^2$
For the $z$ terms: $-8z - (-7z) = -8z + 7z = (-8 + 7)z = -1z$
For the constant terms: $2 - 4 = -2$

STEP 5

Combine the results of the subtraction to get the final polynomial.
$2z^2 - 1z - 2$

STEP 6

Simplify the polynomial by removing the coefficient of 1 in front of $z$ .
$2z^2 - z - 2$
This is the result of the subtraction.

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Question Subtract $6 z^{2} - 8 z + 2$ and $-(4 z^{2} + 7 z - 4)$ .

Studdy Solution

STEP 1

Assumptions
1. We are given two polynomials: $6z^2 - 8z + 2$ and $4z^2 + 7z - 4$ .
2. We need to subtract the second polynomial from the first one.

STEP 2

Write down the given polynomials, aligning like terms.
$\begin{array}{r} 6z^2 - 8z + 2 \\ -(4z^2 + 7z - 4) \\ \end{array}$

STEP 3

Distribute the negative sign across the second polynomial.
$\begin{array}{r} 6z^2 - 8z + 2 \\ -4z^2 - 7z + 4 \\ \end{array}$

STEP 4

Subtract the coefficients of the like terms.
For the $z^2$ terms: $6z^2 - 4z^2 = (6 - 4)z^2 = 2z^2$
For the $z$ terms: $-8z - (-7z) = -8z + 7z = (-8 + 7)z = -1z$
For the constant terms: $2 - 4 = -2$

STEP 5

Combine the results of the subtraction to get the final polynomial.
$2z^2 - 1z - 2$

STEP 6

Simplify the polynomial by removing the coefficient of 1 in front of $z$ .
$2z^2 - z - 2$
This is the result of the subtraction.

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Question Subtract 6z2−8z+26 z^{2} - 8 z + 26z2−8z+2 and −(4z2+7z−4)-(4 z^{2} + 7 z - 4)−(4z2+7z−4).

Studdy Solution

STEP 1

Assumptions1. We are given two polynomials: 6z2−8z+26z^2 - 8z + 26z2−8z+2 and 4z2+7z−44z^2 + 7z - 44z2+7z−4.2. We need to subtract the second polynomial from the first one.

STEP 2

Write down the given polynomials, aligning like terms.6z2−8z+2−(4z2+7z−4) \begin{array}{r} 6z^2 - 8z + 2 \\ -(4z^2 + 7z - 4) \\ \end{array} 6z2−8z+2−(4z2+7z−4)​

STEP 3

Distribute the negative sign across the second polynomial.6z2−8z+2−4z2−7z+4 \begin{array}{r} 6z^2 - 8z + 2 \\ -4z^2 - 7z + 4 \\ \end{array} 6z2−8z+2−4z2−7z+4​

STEP 4

STEP 5

Combine the results of the subtraction to get the final polynomial.2z2−1z−22z^2 - 1z - 22z2−1z−2

STEP 6

Simplify the polynomial by removing the coefficient of 1 in front of zzz.2z2−z−22z^2 - z - 22z2−z−2This is the result of the subtraction.

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Question Subtract $6 z^{2} - 8 z + 2$ and $-(4 z^{2} + 7 z - 4)$ .

Assumptions
1. We are given two polynomials: $6z^2 - 8z + 2$ and $4z^2 + 7z - 4$ .
2. We need to subtract the second polynomial from the first one.

Write down the given polynomials, aligning like terms.
$\begin{array}{r} 6z^2 - 8z + 2 \\ -(4z^2 + 7z - 4) \\ \end{array}$

Distribute the negative sign across the second polynomial.
$\begin{array}{r} 6z^2 - 8z + 2 \\ -4z^2 - 7z + 4 \\ \end{array}$

Combine the results of the subtraction to get the final polynomial.
$2z^2 - 1z - 2$

Simplify the polynomial by removing the coefficient of 1 in front of $z$ .
$2z^2 - z - 2$
This is the result of the subtraction.