ADDING BINOMIALS

A mathematical expression containing only two terms which are in addition or subtraction is called binomial. 

Examples :

x - 3

2x + y

p - 2q

Example 1 :

Add :

(x + 3) + (3x + 5)

Solution :

= (x + 3) + (3x + 5)

= x + 3 + 3x + 5

Group the like terms.

= (x + 3x) + (3 + 5)

Combine the like terms.

= 4x + 8

Example 2 :

Add :

(y + 7) + (y - 2)

Solution :

= (y + 7) + (y - 2)

= y + 7 + y - 2

Group the like terms.

= (y + y) + (7 - 2)

Combine the like terms.

= 2y + 5

Example 3 :

Add :

(3z - 3) + (z + 5)

Solution :

= (3z - 3) + (z + 5)

= 3z - 3 + z + 5

Group the like terms.

= (3z + z) + (-3 + 5)

Combine the like terms.

= 4z + 2

Example 4 :

Add :

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

Solution :

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

= 2k - 5 + 5k - 3

Group the like terms.

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

Combine the like terms.

= 7k + (-8)

= 7k - 8

Example 5 :

Add :

(5x - 1) + (3 - 2x)

Solution :

= (5x - 1) + (3 - 2x)

= 5x - 1 + 3 - 2x

Group the like terms.

= (5x - 2x) + (-1 + 3)

Combine the like terms.

= 3x + 2

Example 6 :

Add :

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

Solution :

= (2y + 3) + (7 - 5y)

= 2y + 3 + 7 - 5y

Group the like terms.

= (2y - 5y) + (3 + 7)

Combine the like terms.

= -3y + 10

Example 7 :

Add :

(z - 7) + (2z + 1)

Solution :

= (z - 7) + (2z + 1)

= z - 7 + 2z + 1

Group the like terms.

= (z + 2z) + (-7 + 1)

Combine the like terms.

= 3z + (-6)

= 3z - 6

Example 8 :

Add :

(p + 2q) + (3p + q)

Solution :

= (p + 2q) + (3p + q)

= p + 2q + 3p + q

Group the like terms.

= (p + 3p) + (2q + q)

Combine the like terms.

= 4p + 3q

Example 9 :

Add :

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

Solution :

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

= 3x + 2y + 5x - 2y

Group the like terms.

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

Combine the like terms.

= 8x + 0

= 8x

Example 10 :

Add :

(x² + 3) + (3x² - 1)

Solution :

= (x² + 3) + (3x² - 1)

= x² + 3 + 3x² - 1

Group the like terms.

= (x² + 3x²) + (3 - 1)

Combine the like terms.

= 4x² + 2

Example 11 :

Add :

(3y² + z) + (2y² - 5z)

Solution :

= (3y² + z) + (2y² - 5z)

= 3y² + z + 2y² - 5z

Group the like terms.

= (3y² + 2y²) + (z - 5z)

Combine the like terms.

= 5y² + (-4z)

= 5y² - 4z

Example 12 :

Add :

(x² - 7x) + (2x² - 3x)

Solution :

= (x² - 7x) + (2x² - 3x)

= x² - 7x + 2x² - 3x

Group the like terms.

= (x² + 2x²) + (-7x - 3x)

Combine the like terms.

= 3x² + (-10x)

= 3x² - 10x

Example 13 :

Add :

(2ab + 3) + (7a + ab)

Solution :

= (2ab + 3) + (7a + ab)

= 2ab + 3 + 7a + ab

Group the like terms.

= (2ab + ab) + 7a + 3

Combine the like terms.

= 3ab + 7a + 3

Example 14 :

Add :

(4x²y - 7) + (1 - 2x²y)

Solution :

= (4x²y - 7) + (1 - 2x²y)

= 4x²y - 7 + 1 - 2x²y

Group the like terms.

= (4x²y - 2x²y) + (-7 + 1)

Combine the like terms.

= 2x²y + (-6)

= 2x²y - 6

Example 15 :

Add :

(2x² - 5xy²) + (x² + 3x²y) + (4xy² - 3x²y)

Solution :

= (2x² - 5xy²) + (x² + 3x²y) + (4xy² - 3x²y)

= 2x² - 5xy² + x² + 3x²y + 4xy² - 3x²y

Group the like terms.

= (2x² + x²) + (3x²y - 3x²y) + (-5xy² + 4xy²)

Combine the like terms.

= 3x² + 0 + (-xy²)

= 3x² - xy²

Practice Questions

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