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Including polynomials by combining like phrases collectively and utilizing algebra tiles is the purpose of this lesson. We’ll present you the next 3 ways so as to add polynomials.

- Utilizing algebra tiles
- Including vertically
- Including horizontally

## Including polynomials with algebra tiles

We’ll begin with algebra tiles because the course of is much more easy and concrete with tiles. To this finish, research the mannequin under with nice care.

**Instance #1:**

Add 2x^{2} + 3x + 4 and 3x^{2} + x + 1

**Step 1**

Mannequin each polynomials with tiles.

**Step 2**

Mix all tiles which can be alike and depend them.

- You bought a complete of 5 mild blue sq. tiles, so 5x
^{2}

- You bought a complete of 4 inexperienced rectangle tiles, so 4x

- You bought a complete of 5 blue small sq. tiles, so 5

Placing all of it collectively, we get 5x^{2} + 4x + 5

I hope from the above modeling, it’s clear that we are able to solely mix tiles of the **identical kind**. For instance, you might not add mild blue sq. tiles to inexperienced rectangle tiles identical to it will not make sense so as to add 5 potatoes to five apples. Attempt including 5 potatoes to five apples and inform me when you bought 10 apples or 10 potatoes. It simply doesn’t make sense!

**Instance #2:**

Add 2x^{2} + -3x + -4 and -3x^{2} + -x + 1

**Step 1**

Mannequin each polynomials with tiles

**Step 2**

Mix all tiles which can be alike and depend them. Tiles which can be alike, however have totally different colours will cancel one another out. We present every cancellation with a inexperienced line.

- You might be left with of 1 purple sq. tile, so -x
^{2}

- You bought a complete of 4 mild purple rectangle tiles, so -4x

- You might be left with 3 robust pink small sq. tiles, so -3

Placing all of it collectively, we get –x^{2} + -4x + -3

## Maintain these essential info in thoughts when including polynomials

- We name tiles which can be alike or are the identical kind “like phrases”

- Like phrases are phrases with the identical variable and the identical exponent. For instance, 2x
^{2}and 3x^{2}in**instance #1**are like phrases as a result of they’ve the identical variable, x and the identical exponent, 2.

- So as to add like time period, simply add the coefficients, or the numbers hooked up to the time period, or the quantity on the left aspect of the time period. 2x
^{2}+ 3x^{2}= (2 + 3)x^{2}= 5x^{2}

## Including polynomials vertically

**Instance #3:**

Add 6x^{2} + 8x + 9 and 2x^{2} + -13x + 2

Line up like phrases. Then add the coefficients.

6x^{2} + 8x + 9

+ 2x^{2} + -13x + 2

——————————

8x^{2} + -5x + 11

Instance #4:

Add -5x^{3} + 4x^{2} + 6x + -8 and 3x^{3} + -2x^{2} + 4x + 12

Line up like phrases. Then add the coefficients.

-5x^{3} + 4x^{2} + 6x + -8

+ 3x^{3} + -2x^{2} + 4x + 12

————————————–

-2x^{3} + 2x^{2} + 10x + 4

## Including polynomials horizontally

**Instance #5:**

Add 6x^{2} + 2x + 4 and 10x^{2} + 5x + 6

Mix or group all like phrases. You may use parentheses to maintain issues organized.

(6x^{2} + 2x + 4) + (10x^{2} + 5x + 6) = (6x^{2} + 10x^{2}) + (2x + 5x) + (4 + 6)

(6x^{2} + 2x + 4) + (10x^{2} + 5x + 6) = (6 + 10)x^{2} + (2 + 5)x + (4 + 6)

Add the coefficient

(6x^{2} + 2x + 4) + (10x^{2} + 5x + 6) = 16x^{2} + 7x + 10

Instance #6:

Add 2x^{4} + 5x^{3} + -x^{2} + 9x + -6 and 10x^{4} + -5x^{3} + 3x^{2} + 6x + 7

(2x^{4} + 5x^{3} + –x^{2} + 9x + -6) + (10x^{4} + -5x^{3} + 3x^{2} + 6x + 7)

= (2x^{4} + 10x^{4}) + (5x^{3} + -5x^{3}) + (-x^{2} + 3x^{2}) + (9x + 6x) + (-6 + 7)

= (2 + 10)x^{4} + (5 + -5)x^{3} + (-1 + 3)x^{2} + (9 + 6)x + (-6 + 7)

= (12)x^{4} + (0)x^{3} + (2)x^{2} + (15)x + (1)

= 12x^{4} + 2x^{2} + 15x + 1

Discover that if the time period is x^{2}, you possibly can rewrite it as 1x^{2}, so your coefficient is 1. We did this in instance #6, third line with (-x^{2} + 3x^{2})

(-x^{2} + 3x^{2}) = (-1x^{2} + 3x^{2})

## Including polynomials quiz

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