Math / Algebra

QuestionCombine the like terms. (Simplify your answer completely.) $13 x^{2}+14 x y+5 y^{2}-3 y^{2}+x^{2}$
Need Help? $\square$

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression by combining similar terms involving $x^2$ , $xy$ , and $y^2$ . Watch out! Don't accidentally combine terms that aren't alike, like $x^2$ and $xy$ !
They're like apples and oranges!

STEP 2

1. Group Like Terms
2. Combine Coefficients

STEP 3

Let's rearrange the expression to put similar terms together.
This makes it way easier to see what we're combining!
Think of it like organizing your sock drawer – all the $x^2$ socks together, the $xy$ socks together, and the $y^2$ socks together!
$13x^2 + x^2 + 14xy + 5y^2 - 3y^2$

STEP 4

Notice how we've grouped the $x^2$ terms, the $xy$ term (all alone, but that's okay!), and the $y^2$ terms.
This sets us up perfectly for the next step!

STEP 5

Now, let's combine those like terms!
For the $x^2$ terms, we have $13x^2$ and $x^2$ , which is like having 13 apples and 1 more apple.
That gives us 14 apples, or in our case, $14x^2$ .
$13x^2 + x^2 = (13+1)x^2 = 14x^2$

STEP 6

The $xy$ term is all by itself, so there's nothing to combine it with.
It's like that unique, single sock that doesn't have a match – still important!
So we have $14xy$ .

STEP 7

Finally, let's tackle the $y^2$ terms.
We have $5y^2$ and $-3y^2$ .
This is like having 5 bananas and taking away 3 bananas, leaving us with 2 bananas, or $2y^2$ .
$5y^2 - 3y^2 = (5-3)y^2 = 2y^2$

STEP 8

Putting it all together, we get:
$14x^2 + 14xy + 2y^2$

STEP 9

Our simplified expression is $14x^2 + 14xy + 2y^2$ !

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QuestionCombine the like terms. (Simplify your answer completely.) $13 x^{2}+14 x y+5 y^{2}-3 y^{2}+x^{2}$
Need Help? $\square$

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression by combining similar terms involving $x^2$ , $xy$ , and $y^2$ . Watch out! Don't accidentally combine terms that aren't alike, like $x^2$ and $xy$ !
They're like apples and oranges!

STEP 2

1. Group Like Terms
2. Combine Coefficients

STEP 3

Let's rearrange the expression to put similar terms together.
This makes it way easier to see what we're combining!
Think of it like organizing your sock drawer – all the $x^2$ socks together, the $xy$ socks together, and the $y^2$ socks together!
$13x^2 + x^2 + 14xy + 5y^2 - 3y^2$

STEP 4

Notice how we've grouped the $x^2$ terms, the $xy$ term (all alone, but that's okay!), and the $y^2$ terms.
This sets us up perfectly for the next step!

STEP 5

Now, let's combine those like terms!
For the $x^2$ terms, we have $13x^2$ and $x^2$ , which is like having 13 apples and 1 more apple.
That gives us 14 apples, or in our case, $14x^2$ .
$13x^2 + x^2 = (13+1)x^2 = 14x^2$

STEP 6

The $xy$ term is all by itself, so there's nothing to combine it with.
It's like that unique, single sock that doesn't have a match – still important!
So we have $14xy$ .

STEP 7

Finally, let's tackle the $y^2$ terms.
We have $5y^2$ and $-3y^2$ .
This is like having 5 bananas and taking away 3 bananas, leaving us with 2 bananas, or $2y^2$ .
$5y^2 - 3y^2 = (5-3)y^2 = 2y^2$

STEP 8

Putting it all together, we get:
$14x^2 + 14xy + 2y^2$

STEP 9

Our simplified expression is $14x^2 + 14xy + 2y^2$ !

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QuestionCombine the like terms. (Simplify your answer completely.) 13x2+14xy+5y2−3y2+x213 x^{2}+14 x y+5 y^{2}-3 y^{2}+x^{2}13x2+14xy+5y2−3y2+x2Need Help? □\square□

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression by combining similar terms involving x2x^2x2, xyxyxy, and y2y^2y2. Watch out! Don't accidentally combine terms that aren't alike, like x2x^2x2 and xyxyxy!They're like apples and oranges!

STEP 2

1. Group Like Terms2. Combine Coefficients

STEP 3

STEP 4

Notice how we've grouped the x2x^2x2 terms, the xyxyxy term (all alone, but that's okay!), and the y2y^2y2 terms.This sets us up perfectly for the next step!

STEP 5

Now, let's **combine** those like terms!For the x2x^2x2 terms, we have 13x213x^213x2 and x2x^2x2, which is like having **13** apples and **1** more apple.That gives us **14** apples, or in our case, 14x214x^214x2.13x2+x2=(13+1)x2=14x213x^2 + x^2 = (13+1)x^2 = 14x^213x2+x2=(13+1)x2=14x2

STEP 6

The xyxyxy term is all by itself, so there's nothing to combine it with.It's like that unique, single sock that doesn't have a match – still important!So we have 14xy14xy14xy.

STEP 7

Finally, let's tackle the y2y^2y2 terms.We have 5y25y^25y2 and −3y2-3y^2−3y2.This is like having **5** bananas and taking away **3** bananas, leaving us with **2** bananas, or 2y22y^22y2.5y2−3y2=(5−3)y2=2y25y^2 - 3y^2 = (5-3)y^2 = 2y^25y2−3y2=(5−3)y2=2y2

STEP 8

Putting it all together, we get:14x2+14xy+2y214x^2 + 14xy + 2y^214x2+14xy+2y2

STEP 9

Our simplified expression is 14x2+14xy+2y214x^2 + 14xy + 2y^214x2+14xy+2y2!

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QuestionCombine the like terms. (Simplify your answer completely.) $13 x^{2}+14 x y+5 y^{2}-3 y^{2}+x^{2}$
Need Help? $\square$

What is this asking? We're asked to simplify an expression by combining similar terms involving $x^2$ , $xy$ , and $y^2$ . Watch out! Don't accidentally combine terms that aren't alike, like $x^2$ and $xy$ !
They're like apples and oranges!

1. Group Like Terms
2. Combine Coefficients

Notice how we've grouped the $x^2$ terms, the $xy$ term (all alone, but that's okay!), and the $y^2$ terms.
This sets us up perfectly for the next step!

Now, let's combine those like terms!
For the $x^2$ terms, we have $13x^2$ and $x^2$ , which is like having 13 apples and 1 more apple.
That gives us 14 apples, or in our case, $14x^2$ .
$13x^2 + x^2 = (13+1)x^2 = 14x^2$

The $xy$ term is all by itself, so there's nothing to combine it with.
It's like that unique, single sock that doesn't have a match – still important!
So we have $14xy$ .

Finally, let's tackle the $y^2$ terms.
We have $5y^2$ and $-3y^2$ .
This is like having 5 bananas and taking away 3 bananas, leaving us with 2 bananas, or $2y^2$ .
$5y^2 - 3y^2 = (5-3)y^2 = 2y^2$

Putting it all together, we get:
$14x^2 + 14xy + 2y^2$

Our simplified expression is $14x^2 + 14xy + 2y^2$ !