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Published on: 10/10/2019
Algebraic Expressions and Identities
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1.
One day, Sahil went to playa cricket tournament (organised in a sports complex) along with his two friends Rahul and Sunil. Someone stole Sahil's bicycle but Rahul and Sunil helped him to buy a new one bicycle contributing rs(2x +80) and rs (8x + 20), respectively, If the bicycle costs rs. 2100,
(a) what were the amount given by Rahul and Sunil to Sahil?
(b) what are the values depicted by Rahul and Sunil here?
2.
The alongside figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.

3.
What must be added to x2+4x+1to make it a whole square?
4.
Find the value of the following products
(i) (2m - n)(m - 2n) at m = 1and n =-1
(ii) (a+2)(b-2) at a=0 and b=-2
5.
Using the formula for squaring a binomial, evaluate the following.(199)2
6.
Find the product of the following binomials.
\(\left( \frac { x-y }{ 2 } \right) \left( \frac { x+y }{ 2 } \right) \)
7.
Find the product of the following binomials.(7x-6y)(7x-6y)
8.
Which of the following polynomials is/are a monomial?\(\frac { 1 }{ 2 } a{ c }^{ 2 }b+ba{ c }^{ 2 }+\frac { 1 }{ 2 } { c }^{ 2 }ab,a+1,abc\)
9.
Classify the following as monomials, binomials and trinomials \(2{ a }^{ 2 }cb+\frac { 1 }{ 2 } cb{ a }^{ 2 },b+1,{ a }^{ 2 }b+{ b }^{ 2 }c+{ c }^{ 2 }a\)
10.
Write down the like terms in the given polynomial \(2c{ a }^{ 2 }+\frac { 1 }{ 2 } b{ c }^{ 2 }a+\frac { 2 }{ 3 } bc{ a }^{ 2 }+3{ a }^{ 2 }bc\)
1.
(a) Rahul contributed =rs(2x + 80)
Sunil contributed = rs(8x + 20)
The total amount=rs[(2x+80)+(8x+20)]
=2100
2x + 8x + 80+ 20 = 2100
10x=2000
x=200
Thus, Rahul's contribution
= 2x + 80= 2 x 200 + 80
= 400 + 80= rs480
and Sunil's contributuib
= 8x + 20 = 8 x 200 + 20
= 1600 + 20 = rs1620
Thus, Rahul's and Sunil contributed rs480 and rs1620 respectively
(b) Rahul and Sunil are very cooperative by nature and they literally proved that "A friend in need is a friend indeed".
2.
According to the given figure
Area of wall = Length\(\times\) Breadth
=(5x + 2) x 5x
= 5x \(\times\) 5x + 5x \(\times\) 2
= 25x2 + 10x sq unit.
Area of window = 2x \(\times\) x = 2x2 sq unit
and area of door = 3x \(\times\) x = 3x2 sq unit
Now, total area of window and door
= 2x2 + 3x2 = 5x2 sq unit
Thus, remaining area of wall to Be painted
=(25x2 + 10x) -(5x2)
= 25x2 + 10x - 5x2 = 20x2 + 10x
=10x(2x+1)sq unit
3.
3
4.
(i)9
(ii)-8
5.
39601
6.
\(\frac { { x }^{ 2 }-{ y }^{ 2 } }{ 4 } \)
7.
49x2-84xy+36y2
8.
\(\frac { 1 }{ 2 } a{ c }^{ 2 }b+ba{ c }^{ 2 }+\frac { 1 }{ 2 } { c }^{ 2 }ab,abc\)
9.
Monomial, binomial, trinomial
10.
\(2c{ a }^{ 2 }b,\frac { 2 }{ 3 } bc{ a }^{ 2 },3{ a }^{ 2 }bc\)
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