ADD SUBTRACT AND MULTIPLY LINEAR EXPRESSIONS

Example 1 :

Add (6a + 3) and (4a - 2).

Solution :

= (6a + 3) + (4a - 2)

 = 6a + 3 + 4a - 2

= 10a + 1

Example 2 :

Add (5y + 8 + 3z) and (4y - 5).

Solution :

= (5y + 8 + 3z) + (4y - 5)

 = 5y + 8 + 3z + 4y - 5

= 9y + 3z + 3

Example 3 :

Subtract (6a - 3b) from (-8a + 9b).

Solution :

= (-8a + 9b) - (6a - 3b)

 = -8a + 9b - 6a + 3b

= -14a + 12b

Example 4 :

Subtract (2x + 3y - 5z) from (5x - 4y - 5z).

Solution :

= (5x - 4y - 5z) - (2x + 3y - 5z)

= 5x - 4y - 5z - 2x - 3y + 5z

= 3x - 7y

Example 5 :

Multiply (3x - 7) and (7x - 3).

Solution :

= (3x - 7)(7x - 3)

= 21x² - 9x - 49x + 21

= 21x² - 58x + 21

Example 6 :

Multiply (3a - 2b) and (2a + 3b).

Solution :

= (3a - 2b)(2a + 3b)

= 6a² + 9ab - 4ab - 6b²

= 6a² + 9ab - 4ab - 6b²

= 6a² + 5ab - 6b²

Example 7 :

Multiply (p + q + r) and (p + q - r).

Solution :

= (p + q + r)(p + q - r)

Let x = p + q.

= (x + r)(x - r)

Using Algebraic Identity a² - b² = (a + b)(a - b),

= x² - r²

Substitute x = p + q.

= (p + q)² - r²

Using Algebraic Identity (a + b)² = a² + 2ab + b².

= p² + 2pq + q² - r²

Example 8 :

Divide (5x + 20) by (5x + 35).

Solution :

= (5x + 20)/(5x + 35)

= [5(x + 4)]/[5(x + 7)]

= (x + 4)/(x + 7)

Example 9 :

Divide (5x - 25) by (3x - 15).

Solution :

= (5x - 25)/(3x - 15)

= 5(x - 5)/3(x - 5)

= 5/3

Example 10 :

Divide (2 - x) by (4x - 8).

Solution :

= (2 - x)/(4x - 8)

= (2 - x)/4(x - 2)

= -(x - 2)/4(x - 2)

= -1/4

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