# MULTIPLYING POLYNOMIALS BOX METHOD

## About "Multiplying polynomials box method"

Multiplying polynomials box method :

Here we are going to see how to multiply polynomials using the box method.

By using this method we can any two polynomials.In this method we need to draw a box which contains some rows and columns.

Here the number of rows depends upon the number of terms of the first polynomial and the number of columns depends upon the number of terms of the second polynomial.

Example 1 :

Multiply the given polynomials using box method

(2x + 8) (6x + 2)

Solution :

Here we use box method to multiply the above polynomials.

The 1st and 2nd polynomial is containing two terms, so the number of rows and number of columns in the box must be 2.

Step 1 :

Step 2 :

Combining the terms

=  12x2 + 4x + 48x + 16

=  12x2 + 52x + 16

Hence the product of the above binomials is 12x2+52x+16

Example 2 :

Multiply the given polynomials using box method

(2x - 3) (3x + 5)

Solution :

Here we use box method to multiply the above polynomials.

The 1st and 2nd polynomial is containing two terms, so the number of rows and number of columns in the box must be 2.

Step 1 :

Step 2 :

Combining the terms

=  6x2 + 10x -9x - 15

=  6x2 + x - 15

Hence the product of the above binomials is 6x2 + x - 15

Example 3 :

Multiply the given polynomials using box method

2x (6x2 - 9xy + y2)

Solution :

Here we use box method to multiply the above polynomials.

In the box,

Number of rows = 1

Number of columns = 3

Step 1 :

Step 2 :

We don't have any like terms

=  12x2 - 18xy + 2xy2

Hence the product of the above binomials is 12x2 - 18xy + 2xy2

Example 4 :

Multiply the given polynomials using box method

(7x - 3)(x2 - 2x + 7)

Solution :

Here we use box method to multiply the above polynomials.

In the box,

Number of rows = 2

Number of columns = 3

Step 1 :

Step 2 :

Combining the like terms

=  7x3 - 14x2 - 3x2 + 49x + 6x - 21

=  7x3 - 17x2 + 55x - 21

Hence the product of the above binomials is 7x3 - 17x+ 55x - 21

Example 5 :

Multiply the given polynomials using box method

(4x + 2)(6x2 - x + 2)

Solution :

Here we use box method to multiply the above polynomials.

In the box,

Number of rows = 2

Number of columns = 3

Step 1 :

Step 2 :

Combining the like terms

=  24x3 - 4x2 +12x2 + 8x - 2x + 4

=  24x3 + 8x+ 6x + 4

Hence the product of the above binomials is 24x3 + 8x+ 6x + 4

After having gone through the stuff given above, we hope that the students would have understood "Multiplying polynomials box method".

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