Question

13) Identify the terms and their coefficient for each of the following expressions.
a) 4xyz² + 3yz
b) x/3 + y/4 - xyz​

Answer 1

Step-by-step explanation:

Expression Terms Coefficients 5xyz2−3zy5xyz2,

−3zy 5

−3 1+x+x21,

x,

x2No coefficient,

1,

1

 4x2y2−4x2y2z2+z2 4x2y2,

−4x2y2z2,

z24, 

−4,

1

 3−pqqr−rp3,

−pq,

−rpNo coefficient,

−1, 

−1 2x+2y−xy2x

2y

−xy

21

21

−1 0.3a−0.6ab+0.5b0.3a

−0.6a

Answer 2

ab - bc) + (bc - ca) + (ca-ab)

= ab + bc + ca - bc - ca - ab

= 0

ii) (a - b + ab) + (b - c + bc) + (c - a + ac)

= a + b + c + ab + bc + ca - b - c - a

= ab + bc + ca

iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2

= (2p2q2 - 3pq + 4) + (5 + 7pq - 3p2q2)

= 2p2q2 - 3p2q2 - 3pq + 7pq + 4 + 5

= - p2q2 + 4pq + 9

iv) (l2 + m2) + (m2 + n2) + (n2 + l2) + (2lm + 2mn + 2nl)

= l2 + l2 + m2 + m2 + n2 + n2 + 2lm + 2mn + 2nl

= 2l2 + 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 4p2q – 3pq + 5pq2 – 8p + 7q – 10

from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q

Answer: 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

i) (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)

= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12

= 8a - 2ab + 2b - 15

ii) (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)

= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx

= 2xy - 7yz + 5zx + 10xyz

iii) (18 - 3p - 11q + 5pq - 2pq2 + 5p2q) - (4p2q - 3pq + 5pq2 - 8p + 7q - 10)

= 18 - 3p - 11q + 5pq - 2pq2 + 5p2q - 4p2q + 3pq - 5pq2 + 8p - 7q + 10

= 28 + 5p - 18q + 8pq - 7pq2 - p2q

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