multiply 2.1x squared yz and 4xyz
Answers
Answer:
1. Identify the terms, their coefficients for each of the following expressions:
(i) 7x2yz – 5xy
(ii) x2 + x + 1
(iii) 3x2y2 – 5x2y2z2 + z2
(iv) 9 – ab + bc – ca
(v) a/2 + b/2 – ab
(vi) 0.2x – 0.3xy + 0.5y
Solution:
(i) 7x2yz – 5xy
The given equation has two terms that are:
7x2yz and – 5xy
The coefficient of 7x2yz is 7
The coefficient of – 5xy is – 5
(ii) x2 + x + 1
The given equation has three terms that are:
x2, x, 1
The coefficient of x2 is 1
The coefficient of x is 1
The coefficient of 1 is 1
(iii) 3x2y2 – 5x2y2z2 + z2
The given equation has three terms that are:
3x2y, -5x2y2z2 and z2
The coefficient of 3x2y is 3
The coefficient of -5x2y2z2 is -5
The coefficient of z2 is 1
(iv) 9 – ab + bc – ca
The given equation has four terms that are:
9, -ab, bc, -ca
The coefficient of 9 is 9
The coefficient of -ab is -1
The coefficient of bc is 1
The coefficient of -ca is -1
(v) a/2 + b/2 – ab
The given equation has three terms that are:
a/2, b/2, -ab
The coefficient of a/2 is 1/2
The coefficient of b/2 is 1/2
The coefficient of -ab is -1
(vi) 0.2x – 0.3xy + 0.5y
The given equation has three terms that are:
0.2x, -0.3xy, 0.5y
The coefficient of 0.2x is 0.2
The coefficient of -0.3xy is -0.3
The coefficient of 0.5y is 0.5
2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
(i) x+y
(ii) 1000
(iii) x+x2+x3+x4
(iv) 7+a+5b
(v) 2b-3b2
(vi) 2y-3y2+4y3
(vii) 5x-4y+3x
(viii) 4a-15a2
(ix) xy+yz+zt+tx
(x) pqr
(xi) p2q+pq2
(xii) 2p+2q
Solution:
(i) x+y
The given expression contains two terms x and y
∴ It is Binomial
(ii) 1000
The given expression contains one term 1000
∴ It is Monomial
(iii) x+x2+x3+x4
The given expression contains four terms
∴ It belongs to none of the categories
(iv) 7+a+5b
The given expression contains three terms
∴ It is Trinomial
(v) 2b-3b2
The given expression contains two terms
∴ It is Binomial
(vi) 2y-3y2+4y3
The given expression contains three terms
∴ It is Trinomial
(vii) 5x-4y+3x
The given expression contains three terms
∴ It is Trinomial
(viii) 4a-15a2
The given expression contains two terms
∴ It is Binomial
(ix) xy + yz + zt + tx
The given expression contains four terms
∴ It belongs to none of the categories
(x) pqr
The given expression contains one term
∴ It is Monomial
(xi) p2q+pq2
The given expression contains two terms
∴ It is Binomial
(xii) 2p+2q
The given expression contains two terms
∴ It is Binomial
EXERCISE 6.2 PAGE NO: 6.5
1. Add the following algebraic expressions:
(i) 3a2b, -4a2b, 9a2b
(ii) 2/3a, 3/5a, -6/5a
(iii) 4xy2 – 7x2y, 12x2y -6xy2, -3x2y + 5xy2
(iv) 3/2a – 5/4b + 2/5c, 2/3a – 7/2b + 7/2c, 5/3a + 5/2b – 5/4c
(v) 11/2xy + 12/5y + 13/7x, -11/2y – 12/5x – 137xy
(vi) 7/2x3 – 1/2x2 + 5/3, 3/2x3 + 7/4x2 – x + 1/3, 3/2x2 -5/2x -2
Solution:
(i) 3a2b, -4a2b, 9a2b
Let us add the given expression
3a2b + (-4a2b) + 9a2b
3a2b – 4a2b + 9a2b
8a2b
(ii) 2/3a, 3/5a, -6/5a
Let us add the given expression
2/3a + 3/5a + (-6/5a)
2/3a + 3/5a – 6/5a
Let us take LCM for 3 and 5 which is 15
(2×5)/(3×5)a + (3×3)/(5×3)a – (6×3)/(5×3)a
10/15a + 9/15a – 18/15a
(10a+9a-18a)/15
a/15
(iii) 4xy2 – 7x2y, 12x2y -6xy2, -3x2y + 5xy2
Let us add the given expression
4xy2 – 7x2y + 12x2y – 6xy2 – 3x2y + 5xy2
Upon rearranging
12x2y – 3x2y – 7x2y – 6xy2 + 5xy2 + 4xy2
3xy2 + 2x2y
(iv) 3/2a – 5/4b + 2/5c, 2/3a – 7/2b + 7/2c, 5/3a + 5/2b – 5/4c
Let us add the given expression
3/2a – 5/4b + 2/5c + 2/3a – 7/2b + 7/2c + 5/3a + 5/2b – 5/4c
Upon rearranging
3/2a + 2/3a + 5/3a – 5/4b – 7/2b + 5/2b + 2/5c + 7/2c – 5/4c
By taking LCM for (2 and 3 is 6), (4 and 2 is 4), (5,2 and 4 is 20)
(9a+4a+10a)/6 + (-5b-14b+10b)/4 + (8c+70c-25c)/20
23a/6 – 9b/4 + 53c/20
(v) 11/2xy + 12/5y + 13/7x, -11/2y – 12/5x – 13/7xy
Let us add the given expression
11/2xy + 12/5y + 13/7x + -11/2y – 12/5x – 13/7xy
Upon rearranging
11/2xy – 13/7xy + 13/7x – 12/5x + 12/5y -11/2y
By taking LCM for (2 and 7 is 14), (7 and 5 is 35), (5 and 2 is 10)
(11xy-12xy)/14 + (65x-84x)/35 + (24y-55y)/10
51xy/14 – 19x/35 – 31y/10
(vi) 7/2x3 – 1/2x2 + 5/3, 3/2x3 + 7/4x2 – x + 1/3, 3/2x2 -5/2x – 2
Let us add the given expression
7/2x3 – 1/2x2 + 5/3 + 3/2x3 + 7/4x2 – x + 1/3 + 3/2x2 -5/2x – 2
Upon rearranging
7/2x3 + 3/2x3 – 1/2x2 + 7/4x2 + 3/2x2 – x – 5/2x + 5/3 + 1/3 – 2
10/2x3 + 11/4x2 – 7/2x + 0/6
5x3 + 11/4x2 -7/2x