Question

Add and find the degree of the following expressions.

(i) (9x + 3y) and (10x – 9y)

(ii) (k² – 25k + 46) and (23 – 2k² + 21 k)

(iii) (3m²n + 4pq²) and (5nm² – 2q²p)

Answer 1

(i) (9x + 3y) and (10x – 9y) 

This can be written as (9x + 3y) + (10x – 9y) 

Grouping the like terms, we get 

(9x + 10x) + (3y – 9y) = x(9 + 10) + y(3 – 0) 

= 19x + y(-6) 

= 19x – 6y 

Thus degree of the expression is 1.

(ii) (k² – 25k + 46) and (23 – 2k² + 21k)

This can be written as (k² – 25k + 46) + (23 – 2k² + 21k)

Grouping the like terms, we get

(k² – 2k²) + (-25 k + 21 k) + (46 + 23)

= k²(1 – 2) + k(-25 + 21) + 69 

= – 1k² – 4k + 69

Thus degree of the expression is 2.

(iii) (3m²n + 4pq²) and (5nm² – 2q²p)

This can be written as (3m²n + 4pq²) + (5nm² – 2q²p)

Grouping the like terms, we get

(3m²n + 5m²n) + (4pq² – 2pq²)

= m²n(3 + 5) + pq²(4 – 2) 

= 8m²n + 2pq²

Thus degree of the expression is 3.