Class 7 Maths Algebraic Expressions | Addition and Subtraction of Algebraic Expressions |

__Addition and Subtraction of Algebraic Expressions__

We can add and subtract the algebraic expressions as follows:

**Adding and Subtracting like terms**

Let we want to add 5x and 7x

Now, 5x + 7x = 5 * x + 7 * x

= (5 + 7) * x [Apply distributive Law]

= 12 * x

= 12x

So, 5x + 7x = 12x

Again let we want to add 3xy, 4xy and 7xy

Now, 3xy + 4xy + 7xy = 3 * xy + 4 * xy + 7 * xy

= (3 + 4 + 7) * xy

= 14 * xy

= 14xy

So, 3xy + 4xy + 7xy = 14xy

Thus, the sum of two or more like terms is a like term with a numerical coefficient equal to the sum of

the numerical coefficients of all the like terms.

Again we want to subtract 5p from 12 p

12p – 5p = 12 * p – 5 * p

= (12 - 5) * p

= 7 * p

= 7p

So, 12p – 5p = 7p

In the same way, we subtract 9pq from 15pq

So, 15pq – 9pq = 6pq

Thus, the difference between two like terms is a like term with a numerical coefficient equal to the

difference between the numerical coefficients of the two like terms

Again unlike terms cannot be added or subtracted the way like terms are added or subtracted.

Ex: When x is added to 10 it gives (x + 10). Similarly, when 10 is subtracted from 7pq, it gives 7pq - 10

**Adding and Subtracting general algebraic expressions**

Let us take some examples:

Ex 1: Add 5x + 7 and 2x + 10

Sum = (5x + 7) + (2x + 10)

= 5x + 7 + 2x + 10

= (5x + 2x) + (7 + 10)

= 7x + 17

Ex 2: Subtract 24xy – 10y – 18x from 30xy + 12y + 14x

Subtraction = 30xy + 12y + 14x – (24xy – 10y – 18x)

= 30xy + 12y + 14x – 24xy + 10y + 18x

= 30xy – 24xy + 12y + 10y + 14x + 18x

= 6xy + 22y + 32x

__Problem: __

(a) What should be added to x^{2} + xy + y^{2} to obtain 2x^{2} + 3xy ?

(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16 ?

Answer:

(a) Let p should be added.

Then, according to question,

=> x^{2} + xy + y^{2} + p = 2x^{2} + 3xy

=> p = 2x^{2} + 3xy – (x^{2} + xy + y^{2})

=> p = 2x^{2} + 3xy – x^{2} - xy - y^{2}

=> p = x^{2} + 2xy - y^{2}

Hence, x^{2} + 2xy - y^{2} should be added.

(b) Let q should be subtracted.

Then, according to question,

2a + 8b + 10 – q = -3a + 7b + 16

=> -q = -3a + 7b + 16 – (2a + 8b + 10)

=> -q = -3a + 7b + 16 – 2a - 8b – 10

=> -q = -5a – b + 6

=> q = -(-5a – b + 6) [Multiply (-) sign on both side]

=> q = 5a + b – 6

Hence, 5a + b – 6 should be subtracted.

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