(3L-0.2)(3L-0.3)
use suatable special products to find the answer
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
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: