[Exercise- Page 69]
E.3.1. Which of the following is not a binomial expression? Explain the logic behind your answer.
a) xy + 3x
b) xy
c) x + y - 1
d) x2 - 2x + 1
e) y2
Solution:
E.3.2. From the binomial expressions below, separate the expressions with one variable and two variables.
a) x + 1
b) 3x + 5
c) x - 3
d) 5x - 2
e) 2x + 3y
f) x2 + 1
g) x2 - y
h) x2 + y2
Solution:
E.3.3. From the algebraic expressions below, determine the trinomial expressions of one, two and three variables respectively.
a) x + y + 3
b) x2 + 3x + 5
c) xy + z - 3
d) 5x + y2 - 2
e) 2x + 3y - z
f) y2 - y + 1
g) x2 - yz + 2
h) x2 + y2 - 2
Solution:
E.3.4. Calculate the cubes of following trinomial expressions.
a) x + y + 3
b) 2x + 3y - z
c) x2 + 3x + 5
d) xy + z - 3
Solution:
E.3.5. Factorize the expressions using algebraic rules:
a) x3 + 1
b) x3 - 1
c) x6 - 729
d) x3 + 3x2 + 3x + 9
Solution:
E.3.6. In a chocolate factory, raw materials are kept in two cubic shaped containers of length 2 ft and 3 ft respectively to their full capacity.
a) If no raw material is lost/damaged, how many chocolates of size 1” × 1” × 2” can be produced by taking all the raw materials of the two containers.
b) If no raw material is lost/damaged, how many chocolates of size 5” × 7” × 1” can be produced by taking all the raw materials of the two containers.
c) If 1440 chocolate bars of size 5” × 7” × 1” are produced using the raw materials of the two containers, how much of the raw materials are wasted?
Solution:
E.3.7. Suppose Lata’s father has a fish farm. There is a pond in the farm which is 50 meters long, 40 meters wide and 5 meters deep. Keeping the volume fixed, if we want to reduce the depth by 3 meters, how long the length is needed to be increased?
Solution:
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