Solved on Jan 24, 2024

Simplify $5x^2 + 7x - 2x^2 + 9y + 8y^2 - 3x$ .

STEP 1

Assumptions
1. We are given a polynomial expression: $5x^{2}+7x-2x^{2}+9y+8y^{2}-3x$ .
2. We need to combine like terms to simplify the expression.

STEP 2

Identify like terms in the expression. Like terms are terms that contain the same variables raised to the same power.

STEP 3

Combine the like terms that contain $x^{2}$ :
$5x^{2} - 2x^{2} = (5 - 2)x^{2} = 3x^{2}$

STEP 4

Combine the like terms that contain $x$ :
$7x - 3x = (7 - 3)x = 4x$

STEP 5

Combine the like terms that contain $y$ and $y^{2}$ . Note that $y$ and $y^{2}$ are not like terms and cannot be combined.

STEP 6

There are no like terms for $y$ , so we leave the $9y$ as it is.

STEP 7

There are no like terms for $y^{2}$ , so we leave the $8y^{2}$ as it is.

STEP 8

Write down the simplified expression by combining the results from steps 3, 4, 6, and 7:
$3x^{2} + 4x + 9y + 8y^{2}$
The expression is fully simplified.

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Simplify $5x^2 + 7x - 2x^2 + 9y + 8y^2 - 3x$ .

STEP 1

Assumptions
1. We are given a polynomial expression: $5x^{2}+7x-2x^{2}+9y+8y^{2}-3x$ .
2. We need to combine like terms to simplify the expression.

STEP 2

Identify like terms in the expression. Like terms are terms that contain the same variables raised to the same power.

STEP 3

Combine the like terms that contain $x^{2}$ :
$5x^{2} - 2x^{2} = (5 - 2)x^{2} = 3x^{2}$

STEP 4

Combine the like terms that contain $x$ :
$7x - 3x = (7 - 3)x = 4x$

STEP 5

Combine the like terms that contain $y$ and $y^{2}$ . Note that $y$ and $y^{2}$ are not like terms and cannot be combined.

STEP 6

There are no like terms for $y$ , so we leave the $9y$ as it is.

STEP 7

There are no like terms for $y^{2}$ , so we leave the $8y^{2}$ as it is.

STEP 8

Write down the simplified expression by combining the results from steps 3, 4, 6, and 7:
$3x^{2} + 4x + 9y + 8y^{2}$
The expression is fully simplified.

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Simplify 5x2+7x−2x2+9y+8y2−3x5x^2 + 7x - 2x^2 + 9y + 8y^2 - 3x5x2+7x−2x2+9y+8y2−3x.

STEP 1

Assumptions1. We are given a polynomial expression: 5x2+7x−2x2+9y+8y2−3x5x^{2}+7x-2x^{2}+9y+8y^{2}-3x5x2+7x−2x2+9y+8y2−3x.2. We need to combine like terms to simplify the expression.

STEP 2

Identify like terms in the expression. Like terms are terms that contain the same variables raised to the same power.

STEP 3

Combine the like terms that contain x2x^{2}x2:5x2−2x2=(5−2)x2=3x25x^{2} - 2x^{2} = (5 - 2)x^{2} = 3x^{2}5x2−2x2=(5−2)x2=3x2

STEP 4

Combine the like terms that contain xxx:7x−3x=(7−3)x=4x7x - 3x = (7 - 3)x = 4x7x−3x=(7−3)x=4x

STEP 5

Combine the like terms that contain yyy and y2y^{2}y2. Note that yyy and y2y^{2}y2 are not like terms and cannot be combined.

STEP 6

There are no like terms for yyy, so we leave the 9y9y9y as it is.

STEP 7

There are no like terms for y2y^{2}y2, so we leave the 8y28y^{2}8y2 as it is.

STEP 8

Write down the simplified expression by combining the results from steps 3, 4, 6, and 7:3x2+4x+9y+8y23x^{2} + 4x + 9y + 8y^{2}3x2+4x+9y+8y2The expression is fully simplified.

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

Simplify $5x^2 + 7x - 2x^2 + 9y + 8y^2 - 3x$ .

Assumptions
1. We are given a polynomial expression: $5x^{2}+7x-2x^{2}+9y+8y^{2}-3x$ .
2. We need to combine like terms to simplify the expression.

Combine the like terms that contain $x^{2}$ :
$5x^{2} - 2x^{2} = (5 - 2)x^{2} = 3x^{2}$

Combine the like terms that contain $x$ :
$7x - 3x = (7 - 3)x = 4x$

Combine the like terms that contain $y$ and $y^{2}$ . Note that $y$ and $y^{2}$ are not like terms and cannot be combined.

There are no like terms for $y$ , so we leave the $9y$ as it is.

There are no like terms for $y^{2}$ , so we leave the $8y^{2}$ as it is.

Write down the simplified expression by combining the results from steps 3, 4, 6, and 7:
$3x^{2} + 4x + 9y + 8y^{2}$
The expression is fully simplified.