Distribute Polynomials - Polynomials Lesson 3 - Algebra 1

1. Perform the indicated operations:

a. (7k – 2) + 3(k + 5)

b. (7k – 2) – 3(k + 5)

Multiple Choice

(7k - 2) + 3(k + 5)

• 7k - 2 + 3k + 15

• 10k - 13

• 4k - 17

• 10k + 13

Multiple Choice

(7k - 2) - 3(k + 5)

• 7k - 2 + 3k + 15

• 10k - 13

• 4k - 17

• 10k + 13

Today we will extend what we learned about multiplying
polynomials. It’s the same concept with a further application.

Today we will extend what we learned about multiplying
polynomials. It’s the same concept with a further application.

Keep in Mind: Distributing is just multiplication. Just like division was
taught/learned after multiplication, we will be doing something called
factoring, which is “undistributing.”

Factoring is breaking something down into its multiplicative parts, like 12 = 3 × 4.

Match

Match the following numbers with their factors.

• Multiples not factors

• 6

• 12

• 7

• 8

6, 12, 18, 24, ...

1, 6 and 2, 3

1, 12, and 3,4, and 2, 6

1, 7

2, 2, 2 are the prime factors

• 6, 12, 18, 24, ...

• 1, 6 and 2, 3

• 1, 12, and 3,4, and 2, 6

• 1, 7

• 2, 2, 2 are the prime factors

4x(5x + 2) means 4x times everything in the parenthesis.

That means 4x × 5x PLUS 4x × 2.

Evaluate: 4x(5x + 2)

Drag and Drop

Evaluate 4x(5x + 2) = ​ ​ $$20x^{2\ }+8x$$

Drag these tiles and drop them in the correct blank above

20x + 8

Example: (4𝑥 − 3)(5𝑥 + 2)

Remember, multiplication is

sometimes written without a symbol.
In this example, we are being told to
multiply everything in the first set of

parenthesis with everything in the

second set of parenthesis.

Example: (4𝑥 − 3)(5𝑥 + 2)

Remember, multiplication is

sometimes written without a symbol.
In this example, we are being told to
multiply everything in the first set of

parenthesis with everything in the

second set of parenthesis.

4x(5x + 2) – 3(5x + 2)

Let’s finish this one together.

(8k + 3)(2k – 1)

Step

Work

Set up the
distribution

Distribute

Combine Like
Terms

Write in
Descending Order

Example:

(8k + 3)(2k – 1)

Step

Work

Set up the
distribution

Distribute

Combine Like
Terms

Write in
Descending Order

Example:

8k(2k – 1) + 3(2k – 1)

(8k + 3)(2k – 1)

Step

Work

Set up the
distribution

Distribute

Combine Like
Terms

Write in
Descending Order

Example:

8k(2k – 1) + 3(2k – 1)

16k2– 8k + 6k – 3

(8k + 3)(2k – 1)

Step

Work

Set up the
distribution

Distribute

Combine Like
Terms

Write in
Descending Order

already in descending order

Example:

8k(2k – 1) + 3(2k – 1)

16k2– 8k + 6k – 3

16k2– 2k – 3

(k + 3)( k2+ 2k + 6)

Step

Work

Set up the
distribution

Distribute

Combine Like
Terms

Write in
Descending Order

(k + 3)( k2+ 2k + 6)

Step

Work

Set up the
distribution

k(k2+ 2k + 6) + 3(k2+ 2k + 6)

Distribute

Combine Like
Terms

Write in
Descending Order

(k + 3)( k2+ 2k + 6)

Step

Work

Set up the
distribution

k(k2+ 2k + 6) + 3(k2+ 2k + 6)

Distribute

k3+ 2k2+ 6k + 3k2+ 6k + 18

Combine Like
Terms

Write in
Descending Order

(k + 3)( k2+ 2k + 6)

Step

Work

Set up the
distribution

k(k2+ 2k + 6) + 3(k2+ 2k + 6)

Distribute

k3+ 2k2+ 6k + 3k2+ 6k + 18

Combine Like
Terms

k3+ 5k2+ 12k + 18

Write in
Descending Order

Stolen from the
internet … link.

You’re done when you have combined all like terms and

written your answer in descending order.

To square something is to multiply the base by itself.

​Which one is right?

(4x – 2)(x + 3)

4x – 2(x + 3)

Be careful to follow the math that is

written, not some pattern in your head!

Multiple Choice

5x + 3(2x - 7)

• 11x - 21

• $$10x^{2\ }-29x-21$$

• 15x + 21

• 8x - 21

Summary Parenthesis groups terms
together. Two polynomials written side by
side without a sign in between means
multiplication. To multiply you write each of
the terms in the first group times the second
group. Distribute and combined like terms.

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