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Identify the terms, their coefficients for each of the following expressions.

(i)xyz

(ii)1 - x -2x

(iii)4p

(iv)4 - xy + yz - xz

(v) (x/4) - (y/5) -y

(vi)1.3a - 2.6ab + 1.5b

(i) Terms xyz^{2}, 3xy coefficients 1,3

(ii)Terms 1,-x,-2x^{2} Coefficients 1, -1,-2

(iii)Terms 4p^{2}q^{2},-4p^{2}q^{2}r^{2},r^{2} Coefficients 4,-4,1

(iv) Terms 4,-xy,yz,-xz Coefficients 4,-1,1,-1

(v) Terms x/4, -y/5 ,-y Coefficients 1/4,-1/5,-1

(vi) Terms 1.3a,-2.6ab,1.5b Coefficients 1.3,-2.6 ,1.5

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

(a)x

(b)1000-x

(c)x + x

(d)8 - y -5x

(e) 2y -3y

(f) 2y - 3y+ 4y

(g) 5x -8y + 3xy

(h) 4 -15z

(i) ab + bc + cd + da+ 2ab

(j) pqr+2pq+5pqr

(k) p

(l) 2p + 2q+1

(a)x^{2} + y^{2}: Binomial

(b)1000-x:Binomial

(c)x + x^{2}+ x^{3} + x^{4} + x^{5}:polynomial

(d)8 - y -5x:Trinomial

(e) 2y -3y^{2}:Binomial

(f) 2y - 3y+ 4y^{3}:Trinomial

(g) 5x -8y + 3xy:Trinomial

(h) 4 -15z^{2}:Binomial

(i) ab + bc + cd + da+ 2ab:polynomial

(j) pqr+2pq+5pqr:Binomial

(k) p^{2}q + pq^{2}:Binomial

(l) 2p + 2q+1:Trinomial

Add the following.

(i) ab - bc+ ac, bc - ca+ ab, ca - ab-2bc

(ii)p - q + pq, q - r + qr, r - p + pr , p+q+r

(iii)2p

(iv)a

(i) ab - bc+ ac + bc - ca+ ab +ca - ab-2bc=ab-2bc+ac

(ii)p - q + pq + q - r + qr + r - p + pr + p+q+r=p+q+pq+r+qr+pr

(iii)2p^{2}q^{2}- 3pq + 4 + 5 + 7pq - 3p^{2}q^{2} + 4p^{2}q^{2} + 10pq=3p^{2}q^{2}+14pq+9

(iv) a^{2}+ b^{2}+ b^{2}+ c^{2}+ c^{2}+ a^{2}+ 2ab + 2bc + 2ac=2(a^{2}+ b^{2}+c^{2}+ab+bc+ac)

(a) Subtract 8a - 7ab + 3b - 20 from 20a - 9ab + 5b - 20

(b) Subtract 3pq + 5qr - 7pr+1 from -4pq +2qr - 2pr + 5pqr+1

(c) Subtract 4p

from 18 - 3p - 11q + 5pq - 2pq

While subtracting, we need to remember signs are reversed after sign once bracket is opened
ie. + becomes - and - becomes +
Let solve the below question keeping that in mind
(a) 20a - 9ab + 5b - 20 -(8a - 7ab + 3b - 20)=20a - 9ab + 5b - 20-8a +7ab-3b+20 =12a+2b -2ab

(b) -4pq +2qr - 2pr + 5pqr+1 -( 3pq + 5qr - 7pr+1 )=-4pq +2qr - 2pr + 5pqr+1 -3pq-5qr+7pr-1=-7pq -3qr+5pr+5pqr

(c) 18 - 3p - 11q + 5pq - 2pq^{2}+ 5p^{2}q -(4p^{2}q - 4pq - 5pq^{2} - 8p + 7q - 18)= 18 - 3p - 11q + 5pq - 2pq^{2}+ 5p^{2}q -4p^{2}q+4pq +5pq^{2}+8p-7q+18=36-3p-18q+9pq+3pq^{2}+5p^{2}q -4p^{2}q

What are the coefficient of each term in the below expression?

4p

(a)4,4,-1,5

(b)4,4,1,5

(c) 4,4r

(d) None of these

Answer is (a)

The product of a monomial and trinomial will be a

(a)monomial

(b)trinomial

(c)binomial

(d) None of these

Answer is (b)

The exponents of a variable term in the polynomial is a

(a) integers

(b)negative integers

(c) positive integers

(d) non -negative integers

Answer is (d)

The expression pqr +rqp+qpr is a

(a) Monomial

(b)trinomial

(c) binomial

(d) none of these

Answer is (a) as it sums to 3pqr

Sum of a - b + ab, b + c - bc and c - a - ac is

(a) 2c + ab - ac - bc

(b) 2c - ab - ac - bc

(c) 2c + ab + ac + bc

(d) 2c - ab + ac + bc

Answer is (a) as it sums to 2c + ab ac bc

The value of $(a + b)^2 + (a - b)^2$ is

(a) 2a + 2b

(b) 2a - 2b

(c) $2a^2 + 2b^2$

(d) $2a^2 - 2b^2$

Answer is (c) as $(a + b)^2 + (a - b)^2=a^2 + b^2 + 2ab +a^2 + b^2 - 2ab=2a^2 + 2b^2$

(p) -> (iii) (q) -> (iv) (r) -> (ii) (s) -> (i)

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