Add and find the degree of the following expressions.(i) (9x + 3y) and

1.	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» (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.

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»

(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.