# Multiplication of Algebraic Terms with Powers (2)

In this worksheet, students must multiply more complicated algebraic terms.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:

### QUESTION 1 of 10

This worksheet is about the multiplication of algebraic terms with powers.

Example

Simplify:

2a3b × 5a4b2

Remember what 2a3b and 5a4b2 means and multiply them.

We get:

2 × a × a × a × b × 5 × a × a × a × a × b × b

Bring the numbers to the front and separate the letters to get:

2 × 5 × a × a × a × a × a × a × a × b × b × b

This gives us

10 × a × a × a × a × a × a × a × b × b × b

which simplifies to

10a7b3

Quick method

Simplify:

2a3b × 5a4b2

Multiply the numbers (2 × 5 = 10).

Add the indices of identical letters (for a: 3 + 4 = 7 and for b: 1 + 2 = 3).

Simplify:

2a3b × 3a4b3

6a7b4

5a7b

6a7b3

Simplify:

2a3b2 × 3a2b3

6a6b6

5a5b5

6a5b5

Simplify:

2a3b2 × a4b2

2a12b4

2a7b4

a12b4

Simplify:

2c3b4 × 4c4b5

6c12b20

8c7b9

c12b9

Simplify:

3c3b3 × 4c4b4

7c12b12

12c12b12

12c7b7

Simplify:

4p3q4 × 4p3q4

16p9q16

16p6q8

8p9q16

Simplify:

4p3q4 × 4p4q3

16p7q7

16p6q8

8p9q16

Simplify:

2p5r × 5p2r5

10p7r6

10p10r5

10p10r0

Simplify:

4p5q4 × 5p2q5

20p7q20

20p10q20

20p7q9

Simplify:

2p5r × 5p2r5

10p7r6

10p10r5

10p10r0

• Question 1

Simplify:

2a3b × 3a4b3

6a7b4
EDDIE SAYS
2 × 3 × a × a × a × a × a × a × a × b × b × b × b
• Question 2

Simplify:

2a3b2 × 3a2b3

6a5b5
EDDIE SAYS
2 × 3 × a × a × a × a × a × b × b × b × b × b
• Question 3

Simplify:

2a3b2 × a4b2

2a7b4
EDDIE SAYS
2 × a × a × a × a × a × a × a × b × b × b × b
• Question 4

Simplify:

2c3b4 × 4c4b5

8c7b9
EDDIE SAYS
2 × 4 × c × c × c × c × c × c × c × b × b × b × b × b × b × b × b × b
• Question 5

Simplify:

3c3b3 × 4c4b4

12c7b7
EDDIE SAYS
3 × 4 × c × c × c × c × c × c × c × b × b × b × b × b × b × b
• Question 6

Simplify:

4p3q4 × 4p3q4

16p6q8
EDDIE SAYS
4 × 4 × p × p × p × p × p × p × q × q × q × q × q × q × q × q
• Question 7

Simplify:

4p3q4 × 4p4q3

16p7q7
EDDIE SAYS
4 × 4 × p × p × p × p × p × p × p × q × q × q × q × q × q × q
• Question 8

Simplify:

2p5r × 5p2r5

10p7r6
EDDIE SAYS
2 × 5 × p × p × p × p × p × p × p × r × r × r × r × r × r
• Question 9

Simplify:

4p5q4 × 5p2q5

20p7q9
EDDIE SAYS
4 × 5 × p × p × p × p × p × p × p × q × q × q × q × q × q × q × q × q
• Question 10

Simplify:

2p5r × 5p2r5

10p7r6
EDDIE SAYS
2 × 5 × p × p × p × p × p × p × p × r × r × r × r × r × r
---- OR ----

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