# Subtraction of Algebraic Expression

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1) Change the signs.

**~ez_lsquo+ez_rsquo~**--->

**‘- ‘**

**‘-‘**----->

**~ez_rsquo+ez_rsquo~**of all the expressions which is to be subtracted and then the two expressions are added.

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2)Then add two expressions.

**Example :**

1) Subtract -7x from 5x

**Solution :**

= 5x – ( -7x)

=5x + 7x

= 12x

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2)x

^{2}+ y

^{2}+ 3xy from 4x

^{2}+ 2xy – 3y

^{2}

**Solution :**

=(4x

^{2}+ 2xy – 3y

^{2}) – (x

^{2}+ y

^{2}+ 3xy)

= 4x

^{2}+ 2xy – 3y

^{2}- x

^{2}- y

^{2}- 3xy

= 4x

^{2}

__+ 2xy__– 3y

^{2}- x

^{2}– y

^{2}

__- 3xy__

= 3x

^{2}- xy – 4y

^{2}

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3)What should be subtracted from a

^{3}- 4a

^{2}+ 5a – 6 to obtain

a

^{2}- 2a + 1 ?

**Solution:**

Let 'X' denote the required expression,

(a

^{3}- 4a

^{2}+ 5a – 6) – X = a

^{2}- 2a + 1

Hence , X = (a

^{3}- 4a

^{2}+ 5a – 6) – (a

^{2}- 2a + 1)

= a

^{3}- 4a

^{2}+ 5a – 6 - a

^{2}+ 2a – 1

= a

^{3}

__- 4a__

^{2}+5a – 6

__- a__

^{2}+2a –1

= a

^{3}- 5a

^{2}+ 7a – 7

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4)Subtract a

^{3}- 4a

^{2}+ 5a – 6 from the sum of 3a

^{3}+ a

^{2}+ 1 and a

^{2}-2?

**Solution:**

= [(3a

^{3}+ a

^{2}+ 1) + a

^{2}-2)] - (a

^{3}- 4a

^{2}+ 5a – 6 )

= (3a

^{3}

__+ a__+ 1 +

^{2}__a__-2 ) - (a

^{2}^{3}- 4a

^{2}+ 5a – 6 )

= (3a

^{3}+ 2a

^{2}-1) - (a

^{3}- 4a

^{2}+ 5a – 6 )

= 3a

^{3}+ 2a

^{2}-1 - a

^{3}+ 4a

^{2}- 5a + 6

=

__3a__+ 2a

^{3}^{2}-1

__- a__+ 4a

^{3}^{2}- 5a + 6

= 2a

^{3}+ 6a

^{2}- 5a + 5

**Algebraic Expressions**

• Like and Unlike terms in Algebra

• Addition of algebraic expressions

• Subtraction of algebraic expressions

• Multiplication of algebraic expressions

• Division of algebraic expressions

• Like and Unlike terms in Algebra

• Addition of algebraic expressions

• Subtraction of algebraic expressions

• Multiplication of algebraic expressions

• Division of algebraic expressions

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