Find the numerical coefficient of each of the terms:

(i) x³y²z, xy²z³, –3xy²z³, 5x³y²z, –7x²y²z²

(ii) 10xyz, –7xy²z, –9xyz, 2xy²z, 2x²y²z²

Write the following statements in the form of algebraic expressions and write whether it is monomial, binomial or trinomial.

(a) x is multiplied by itself and then added to the product of x and y.

(b) Three times of p and two times of q are multiplied and then subtracted from r.

(c) Product of p, twice of q and thrice of r.

(d) Sum of the products of a and b, b and c and c and a.

(e) Perimeter of an equilateral triangle of side x.

(f) Perimeter of a rectangle with length p and breadth q.

(g) Area of a triangle with base m and height n.

(h) Area of a square with side x.

(i) Cube of s subtracted from cube of t.

(j) Quotient of x and 15 multiplied by x.

(k) The sum of square of x and cube of z.

(l) Two times q subtracted from cube of q.

Write the coefficient of x2 in the following:

(i) x² – x + 4

(ii) x³ – 2x² + 3x + 1

(iii) 1 + 2x + 3x² + 4x³

(iv) y + y²x + y³x² + y⁴x³

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

(a) 3x²yz² – 3xy²z + x²yz² + 7xy²z

(b) x⁴ + 3x³y+3x²y²–3x³y–3xy³+y⁴– 3x²y²

(c) p³q²r + pq²r³ + 3p²qr² – 9p²qr²

(d) 2a + 2b+2c–2a–2b–2c – 2b + 2c + 2a

(e) 50x³ – 21x + 107 + 41x³ – x + 1 – 93 + 71x–31x³

Add the following expressions:

(a) p² – 7pq – q² and – 3p² – 2pq + 7q²

(b) x³–x²y–xy² –y³ and x³ –2x²y+3xy²+4y

(c) ab + bc + ca and – bc – ca – ab

(d) p² – q + r, q² – r + p and r² – p + q

(e) x³y² + x²y³ +3y⁴ and x⁴ + 3x²y³ + 4y⁴

(f) p²qr + pq²r + pqr² and – 3pq²r –2pqr²

(g) uv – vw, vw – wu and wu – uv

(h) a² + 3ab – bc, b² + 3bc – ca and c² + 3ca – ab

(i) p⁴ + 2p² + -17p + p² and

(j) t – t² – t³ – 14; 15t³ + 13 + 9t – 8t²; 12t² – 19 – 24t and 4t – 9t² + 19t³