Math / Algebra

Question13. Modélise cette soustraction $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ à l'aide d'un schéma.

Studdy Solution

STEP 1

What is this asking? We need to subtract two expressions, which are groups of terms with $x$ and $x^2$ , and model this subtraction visually! Watch out! Be super careful with those minus signs; they can be tricky!
Double negatives can turn into positives, so keep your eyes peeled!

STEP 2

1. Rewrite the expression
2. Distribute the negative sign
3. Combine like terms

STEP 3

Alright, let's rewrite this subtraction problem to make it easier to work with.
We have $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ .
Remember, subtracting a quantity is the same as adding its opposite.

STEP 4

So, we can rewrite our expression as $\left(-3 x^{2}+4 x\right) + \left(-\left(-2 x^{2}-x\right)\right)$ .
We're basically saying, "Instead of subtracting this whole thing, let's add the opposite of this whole thing."

STEP 5

Now, let's distribute that negative sign into the second set of parentheses.
This means we multiply each term inside the parentheses by $-1$ .

STEP 6

So, $-1 \cdot -2x^2$ becomes $+2x^2$ and $-1 \cdot -x$ becomes $+x$ .
See how those double negatives become positives?
Our expression is now $\left(-3 x^{2}+4 x\right) + \left(2 x^{2}+x\right)$ .

STEP 7

Time to combine those like terms!
Like terms are terms that have the same variable raised to the same power.
We've got $x^2$ terms and $x$ terms.

STEP 8

Let's group our like terms: $(-3x^2 + 2x^2) + (4x + x)$ .

STEP 9

Now, let's add the coefficients of the $x^2$ terms: $-3 + 2 = -1$ .
So, we have $-1x^2$ , or simply $-x^2$ .

STEP 10

Next, let's add the coefficients of the $x$ terms: $4 + 1 = 5$ .
So, we have $5x$ .

STEP 11

Putting it all together, our simplified expression is $-x^{2}+5 x$ .
Boom!

STEP 12

The simplified expression representing the subtraction $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ is $-x^2 + 5x$ .

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Question13. Modélise cette soustraction $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ à l'aide d'un schéma.

Studdy Solution

STEP 1

What is this asking? We need to subtract two expressions, which are groups of terms with $x$ and $x^2$ , and model this subtraction visually! Watch out! Be super careful with those minus signs; they can be tricky!
Double negatives can turn into positives, so keep your eyes peeled!

STEP 2

1. Rewrite the expression
2. Distribute the negative sign
3. Combine like terms

STEP 3

Alright, let's rewrite this subtraction problem to make it easier to work with.
We have $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ .
Remember, subtracting a quantity is the same as adding its opposite.

STEP 4

So, we can rewrite our expression as $\left(-3 x^{2}+4 x\right) + \left(-\left(-2 x^{2}-x\right)\right)$ .
We're basically saying, "Instead of subtracting this whole thing, let's add the opposite of this whole thing."

STEP 5

Now, let's distribute that negative sign into the second set of parentheses.
This means we multiply each term inside the parentheses by $-1$ .

STEP 6

So, $-1 \cdot -2x^2$ becomes $+2x^2$ and $-1 \cdot -x$ becomes $+x$ .
See how those double negatives become positives?
Our expression is now $\left(-3 x^{2}+4 x\right) + \left(2 x^{2}+x\right)$ .

STEP 7

Time to combine those like terms!
Like terms are terms that have the same variable raised to the same power.
We've got $x^2$ terms and $x$ terms.

STEP 8

Let's group our like terms: $(-3x^2 + 2x^2) + (4x + x)$ .

STEP 9

Now, let's add the coefficients of the $x^2$ terms: $-3 + 2 = -1$ .
So, we have $-1x^2$ , or simply $-x^2$ .

STEP 10

Next, let's add the coefficients of the $x$ terms: $4 + 1 = 5$ .
So, we have $5x$ .

STEP 11

Putting it all together, our simplified expression is $-x^{2}+5 x$ .
Boom!

STEP 12

The simplified expression representing the subtraction $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ is $-x^2 + 5x$ .

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Question13. Modélise cette soustraction (−3x2+4x)−(−2x2−x)\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)(−3x2+4x)−(−2x2−x) à l'aide d'un schéma.

Studdy Solution

STEP 1

What is this asking? We need to subtract two expressions, which are groups of terms with xxx and x2x^2x2, and model this subtraction visually! Watch out! Be super careful with those minus signs; they can be tricky!Double negatives can turn into positives, so keep your eyes peeled!

STEP 2

1. Rewrite the expression2. Distribute the negative sign3. Combine like terms

STEP 3

Alright, let's **rewrite** this subtraction problem to make it easier to work with.We have (−3x2+4x)−(−2x2−x)\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)(−3x2+4x)−(−2x2−x).Remember, subtracting a quantity is the same as *adding* its opposite.

STEP 4

So, we can **rewrite** our expression as (−3x2+4x)+(−(−2x2−x))\left(-3 x^{2}+4 x\right) + \left(-\left(-2 x^{2}-x\right)\right)(−3x2+4x)+(−(−2x2−x)).We're basically saying, "Instead of subtracting this whole thing, let's add the *opposite* of this whole thing."

STEP 5

Now, let's **distribute** that negative sign into the second set of parentheses.This means we multiply each term inside the parentheses by −1-1−1.

STEP 6

So, −1⋅−2x2-1 \cdot -2x^2−1⋅−2x2 becomes +2x2+2x^2+2x2 and −1⋅−x-1 \cdot -x−1⋅−x becomes +x+x+x.See how those double negatives become positives?Our expression is now (−3x2+4x)+(2x2+x)\left(-3 x^{2}+4 x\right) + \left(2 x^{2}+x\right)(−3x2+4x)+(2x2+x).

STEP 7

Time to **combine** those **like terms**!Like terms are terms that have the same variable raised to the same power.We've got x2x^2x2 terms and xxx terms.

STEP 8

Let's **group** our like terms: (−3x2+2x2)+(4x+x)(-3x^2 + 2x^2) + (4x + x)(−3x2+2x2)+(4x+x).

STEP 9

Now, let's **add** the coefficients of the x2x^2x2 terms: −3+2=−1-3 + 2 = -1−3+2=−1.So, we have −1x2-1x^2−1x2, or simply −x2-x^2−x2.

STEP 10

Next, let's **add** the coefficients of the xxx terms: 4+1=54 + 1 = 54+1=5.So, we have 5x5x5x.

STEP 11

Putting it all together, our **simplified expression** is −x2+5x-x^{2}+5 x−x2+5x.Boom!

STEP 12

The simplified expression representing the subtraction (−3x2+4x)−(−2x2−x)\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)(−3x2+4x)−(−2x2−x) is −x2+5x-x^2 + 5x−x2+5x.

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Question13. Modélise cette soustraction $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ à l'aide d'un schéma.

What is this asking? We need to subtract two expressions, which are groups of terms with $x$ and $x^2$ , and model this subtraction visually! Watch out! Be super careful with those minus signs; they can be tricky!
Double negatives can turn into positives, so keep your eyes peeled!

1. Rewrite the expression
2. Distribute the negative sign
3. Combine like terms

Alright, let's rewrite this subtraction problem to make it easier to work with.
We have $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ .
Remember, subtracting a quantity is the same as adding its opposite.

So, we can rewrite our expression as $\left(-3 x^{2}+4 x\right) + \left(-\left(-2 x^{2}-x\right)\right)$ .
We're basically saying, "Instead of subtracting this whole thing, let's add the opposite of this whole thing."

Now, let's distribute that negative sign into the second set of parentheses.
This means we multiply each term inside the parentheses by $-1$ .

So, $-1 \cdot -2x^2$ becomes $+2x^2$ and $-1 \cdot -x$ becomes $+x$ .
See how those double negatives become positives?
Our expression is now $\left(-3 x^{2}+4 x\right) + \left(2 x^{2}+x\right)$ .

Time to combine those like terms!
Like terms are terms that have the same variable raised to the same power.
We've got $x^2$ terms and $x$ terms.

Let's group our like terms: $(-3x^2 + 2x^2) + (4x + x)$ .

Now, let's add the coefficients of the $x^2$ terms: $-3 + 2 = -1$ .
So, we have $-1x^2$ , or simply $-x^2$ .

Next, let's add the coefficients of the $x$ terms: $4 + 1 = 5$ .
So, we have $5x$ .

Putting it all together, our simplified expression is $-x^{2}+5 x$ .
Boom!

The simplified expression representing the subtraction $\left(-3 x^{2}+4 x\right)-\left(-2 x^{2}-x\right)$ is $-x^2 + 5x$ .