State whether a given pair of terms is of like or unlike terms.

(i) 1, 100 (ii) $-7x,\frac{5}{2}x$ (iii) − 29x, − 29y

(iv) 14xy, 42yx (v) 4m²p, 4mp² (vi) 12xz, 12 x²z²

Identify like terms in the following:

(a) −xy², − 4yx², 8x², 2xy², 7y, − 11x², − 100x, −11yx, 20x²y, −6x², y, 2xy,3x

(b) 10pq, 7p, 8q, − p²q², − 7qp, − 100q, − 23, 12q²p², − 5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Simplify combining like terms:

(i) 21b − 32 + 7b − 20b

(ii) − z² + 13z² − 5z + 7z³ − 15z

(iii) p − (p − q) − q − (q − p)

(iv) 3a − 2b − ab − (a − b + ab) + 3ab + b − a

(v) 5x²y − 5x² + 3y x² − 3y² + x² − y² + 8xy² −3y²

(vi) (3 y² + 5y − 4) − (8y − y² − 4)

Add:

(i) 3mn, − 5mn, 8mn, −4mn

(ii) t − 8tz, 3tz − z, z − t

(iii) − 7mn + 5, 12mn + 2, 9mn − 8, − 2mn − 3

(iv) a + b − 3, b − a + 3, a − b + 3

(v) 14x + 10y − 12xy − 13, 18 − 7x − 10y + 8xy, 4xy

(vi) 5m − 7n, 3n − 4m + 2, 2m − 3mn − 5

(vii) 4x²y, − 3xy², − 5xy², 5x²y

(viii) 3p²q² − 4pq + 5, − 10p²q², 15 + 9pq + 7p²q²

(ix) ab − 4a, 4b − ab, 4a − 4b

(x) x² − y² − 1 , y² − 1 − x², 1− x² − y²

Subtract:

(i) − 5y² from y²

(ii) 6xy from − 12xy

(iii) (a − b) from (a + b)

(iv) a (b − 5) from b (5 − a)

(v) − m² + 5mn from 4m² − 3mn + 8

(vi) − x² + 10x − 5 from 5x − 10

(vii) 5a² − 7ab + 5b² from 3ab − 2a² −2b²

(viii) 4pq − 5q² − 3p² from 5p² + 3q² − pq

(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

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

What should be taken away from 3x² − 4y² + 5xy + 20 to obtain

− x² − y² + 6xy + 20?

(a) From the sum of 3x − y + 11 and − y − 11, subtract 3x − y − 11.

(b) From the sum of 4 + 3x and 5 − 4x + 2x², subtract the sum of 3x² − 5x and − x² + 2x + 5.

If p = −2, find the value of:

(i) 4p + 7

(ii) −3p² + 4p + 7

(iii) −2p³ − 3p² + 4p + 7

Find the value of the following expressions, when x = − 1:

(i) 2x − 7 (ii) − x + 2 (iii) x² + 2x + 1

(iv) 2x² − x − 2