Multiplying polynomials

In this PowerPoint presentation you will see two alternative approaches to polynomial multiplication.To see multiplication using a table click here.

To see multiplication “in your head” click here.

Using a table

x² 3x -2

2x²

-x

4

Multiply x² + 3x – 2 by 2x² – x + 4

Using a table

x² 3x -2

2x²

-x

4

Multiply x² by 2x²

Using a table

x² 3x -2

2x² 2x4

-x

4

Multiply x² by 2x²

Using a table

x² 3x -2

2x² 2x4

-x

4

Multiply 3x by 2x²

Using a table

x² 3x -2

2x² 2x4 6x³

-x

4

Multiply 3x by 2x²

Using a table

x² 3x -2

2x² 2x4 6x³

-x

4

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x

4

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³

4

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x²

4

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x²

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x² 12x

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x² 12x -8

Fill in the rest of the table in the same way

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x² 12x -8

Now add up all the terms in the table

First the term in x4

(x² + 3x – 2)(2x² - x + 4) = 2x4

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x² 12x -8

Now add up all the terms in the table

then the terms in x³

(x² + 3x – 2)(2x² - x + 4) = 2x4 + 5x³

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x² 12x -8

Now add up all the terms in the table

then the terms in x²

(x² + 3x – 2)(2x² - x + 4) = 2x4 + 5x³

- 3x²

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x² 12x -8

Now add up all the terms in the table

(x² + 3x – 2)(2x² - x + 4) = 2x4

then the terms in x

+ 5x³

- 3x² + 14x

Using a table

x² 3x -2

2x² 2x4 6x³ -4x²

-x -x³ -3x² 2x

4 4x² 12x -8

Now add up all the terms in the table

(x² + 3x – 2)(2x² - x + 4) = 2x4

and finally the constant term

+ 5x³

- 3x² + 14x- 8

Multiplying polynomials

To see this example of multiplication using a table again click here.

To see multiplication “in your head” click here.

To end this presentation click here.

Multiplying in your head

Multiply x² + 3x – 2 by 2x² – x + 4

(x² + 3x – 2)(2x² – x + 4)

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Start by multiplying the first terms in each bracket to give a term in x4

= 2x4

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now look for pairs of terms which multiply together to give a term in x³. There are two pairs.

– x³= 2x4

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now look for pairs of terms which multiply together to give a term in x³. There are two pairs.

– x³ + 6x³

= 2x4

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now look for pairs of terms which multiply together to give a term in x². There are three pairs.

– x³ + 6x³

+ 4x²= 2x4

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now look for pairs of terms which multiply together to give a term in x². There are three pairs.

– x³ + 6x³

+ 4x²= 2x4 - 3x²

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now look for pairs of terms which multiply together to give a term in x². There are three pairs.

– x³ + 6x³

+ 4x²- 3x² - 4x²= 2x4

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now look for pairs of terms which multiply together to give a term in x. There are two pairs.

= 2x4 – x³ + 6x³

+ 4x²- 3x² - 4x² + 12x

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now look for pairs of terms which multiply together to give a term in x. There are two pairs.

= 2x4 – x³ + 6x³

+ 4x²- 3x² - 4x² + 12x

+ 2x

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Finally multiply the last two terms in each bracket to give the constant term.

= 2x4 – x³ + 6x³

+ 4x²- 3x² - 4x² + 12x

+ 2x - 8

Multiplying in your head

(x² + 3x – 2)(2x² – x + 4)

Now simplify by collecting like terms.

= 2x4 – x³ + 6x³

+ 4x²- 3x² - 4x² + 12x

+ 2x - 8

= 2x4 + 5x³ - 3x² + 14x - 8

Multiplying polynomials

To see multiplication using a table click here.

To see this example of multiplication “in your head” again click here.

To end this presentation click here.