(3L-0.2)(3L-0.3)
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Answers
Question 1:
Identify the terms, their coefficients for each of the following expressions:
(i) 5xyz2 - 3zy (ii) 1+ x + x2 (iii) 4x2 y2 - 4x2 y2 z2
(iv) 3 - pq + qr - rp (v) x/2 + y/2 - xy (vi) 0.3a - 0.6ab + 0.5b
Answer:
(i) Terms: 5xyz2 and -3zy
Coefficient in 5xyz2 is 5 and in -3zy is -3.
(ii) Terms: 1, x and x2.
Coefficient of x and coefficient of x2 is 1.
(iii) Terms: 4x2 y2, -4 x2 y2 z2 and z2.
Coefficient in 4x2 y2 is 4, coefficient of -4 x2 y2 z2 is -4 and coefficient of z2 is 1.
(iv) Terms: 3, -pq, qr and -rp
Coefficient of –pq is -1, coefficient of qr is 1 and coefficient of –rp is -1.
(v) Terms: x/2, y/2 and and -xy
Coefficient of x/2 is 1/2, coefficient of y/2 is 1/2 and coefficient of –xy is -1.
(vi) Terms: 0.3a, 0.6ab and 0.5b
Coefficient of 0.3a is 0.3, coefficient of -0.6ab is -0.6 and coefficient of 0.5b is 0.5.
Question 2:
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories:
x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y – 3y2 , 2y - 3y + 4y, 5x – 4y + 3xy,
4z – 15z2, ab + bc + cd + da, pqr, p2 q + pq2, 2p + 2q
Answer:
(i) Since x + y contains two terms. Therefore it is binomial.
(ii) Since 1000 contains one term. Therefore it is monomial.
(iii) Since x + x2 + x3 + x4 contains four terms. Therefore it is a polynomial and it does not fit in
above three categories.
(iv) Since 7 + y + 5x contains three terms. Therefore it is trinomial.
(v) Since 2y – 3y2 contains two terms. Therefore it is binomial.
(vi) Since 2y – 3y2 + 4y3 contains three terms. Therefore it is trinomial.
(vii) Since 5x – 4y + 3xy contains three terms. Therefore it is trinomial.
(viii) Since 4x - 15z2 contains two terms. Therefore it is binomial.
(ix) Since ab + bc + cd + da contains four terms. Therefore it is a polynomial and it does not fit
in above three categories.
(x) Since pqr contains one terms. Therefore it is monomial.
(xi) Since p2 q + pq2 contains two terms. Therefore it is binomial.
(xii) Since 2p + 2q contains two terms. Therefore it is binomial.
Question 3:
Add the following:
(i) ab – bc, bc – ca, ca - ab
(ii) a - b + ab, b - c + bc, c - a + ac
(iii) 2p2 q2 - 3pq + 4, 5 + 7pq - 3p2 q2
(iv) l2 + m2, m2 + n2, n2 + l2 + 2lm + 2mn + 2nl
Answer:
(i) ab – bc + bc – ca + ca – ab = ab – ab + bc – bc + ca – ca = 0
(ii) a - b + ab + b - c + bc + c - a + ac
= a – a + b – b + ab + c – c + bc + ac
= ab + bc + ac
(iii) 2p2 q2 - 3pq + 4 + 5 + 7pq - 3p2 q2
= -p2 q2 + 4pq + 9
(iv) l2 + m2 + m2 + n2 + n2 + l2 + 2lm + 2mn + 2nl
= 2 l2 + 2m2 + 2n2 + 2lm + 2mn + 2nl
Question 4:
(a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b - 3
(b) Subtract 3xy + 5yz - 7zx from 5xy – 2yz – 2zx + 10xyz
(c) Subtract 4p2 q - 3pq + 5pq2 - 8p + 7q – 10 from 18 – 3p – 11p + 5pq – 2pq2 + 5p2 q
Answer:
(a) 12a – 9ab + 5b – 3 – (4a – 7ab + 3b + 12)
= 12a – 9ab + 5b – 3 – 4a + 7ab - 3b – 12
= 8a – 2ab + 2b - 15
(b) 5xy – 2yz – 2zx + 10xyz – (3xy + 5yz - 7zx)
= 5xy – 2yz – 2zx + 10xyz – 3xy - 5yz + 7zx
= 2xy – 7yz + 5zx + 10xyz
(c) 18 – 3p – 11p + 5pq – 2pq2 + 5p2 q – (4p2 q - 3pq + 5pq2 - 8p + 7q – 10)
= 18 – 3p – 11p + 5pq – 2pq2 + 5p2 q – 4p2 q + 3pq - 5pq2 + 8p - 7q + 10
= p2 q - 7pq2 + 8pq - 18q + 5p + 28
Exercise 9.2
Question 1:
Find the product of the following pairs of monomials:
(i) 4,7p (ii) -4p, 7p (iii) -4p, 7pq (iv) 4p3, -3p (iv) 4p, 0
Answer:
(i) 4 *7p = 4 * 7 * p = 28p
(ii) -4p * 7p = (-4 * 7) * (p * p) = -28p2
(iii) -4p * 7pq = (-4 * 7) * (p * pq) = -28p2 q
(iv) 4p3 * -3p (4 * -3) * (p3 * p) = -12p4
(iv) 4p * 0 = (4 * 0) * p = 0
Question 2:
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:
(p, q), (10m, 5n), (20x2, 5y2), (4x, 3x), (3mn, 4np)
Answer:
(i) Area of rectangle = length * breadth
= p * q = pq sq. units
(ii) Area of rectangle = length * breadth
= 10m * 5n = 50mn sq. units
(iii) Area of rectangle = length * breadth
= 20x2, 5y2 = 100 x2 y2 sq. units
(iv) Area of rectangle = length * breadth
= 4x * 3x2 = (4 * 3) * (x * x2) = 12x3 sq. units
(v) Area of rectangle = length * breadth
= 3mn * 4np = (3 * 4) * (mn * np) = 12 mn2 p sq. units
Question 3: