Q. 1 To verify the identity (a+b) ^2=a^2+b^2+2ab
Q. 2 To verify the formula for surface area of a cube and Cuboid
Answers
Answer:
CBSE Class 9 Maths Lab Manual – Algebraic Identity (a + b)2 = a2 + 2ab + b2
August 20, 2018 by Bhagya Leave a Comment
CBSE Class 9 Maths Lab Manual – Algebraic Identity (a + b)2 = a2 + 2ab + b2
Objective
To verify the identity (a + b)2 = a2 + 2ab + b2 by paper cutting and pasting.
Prerequisite Knowledge
Area of a square = (side)2.
Area of a rectangle = l x b.
Materials Required
A sheet of white paper, three sheets of glazed paper (different colours), a pair of scissors, gluestick and a geometry box.
Procedure
Take distinct values of a and b, say a = 4 units, b = 2 units
Cut a square of side a (say 4 units) on a glazed paper (blue).
Cut a square of side b (say 2 units) on glazed paper (pink).
Now, cut two rectangles of length a (4 units) and breadth b (2 units) from third glazed paper (red).
CBSE Class 9 Maths Lab Manual – Algebraic Identity (a + b)2 = a2 + 2ab + b2 1
Draw a square PQRS of (a+ b) = (4 + 2), 6 units on white paper sheet as shown in fig. (i).
Paste the squares I and II and two rectangles III and IV on the same white squared paper. Arrange all the pieces on the white square sheet in such a way that they form a square ABCD fig. (ii)
CBSE Class 9 Maths Lab Manual – Algebraic Identity (a + b)2 = a2 + 2ab + b2 2
CBSE Class 9 Maths Lab Manual – Algebraic Identity (a + b)2 = a2 + 2ab + b2 3
Observation
Area of the square PQRS on the white sheet paper.
(a+b)2 = (4+2)2 = 6 x 6 = 36 sq. units ……….(i)
Area of two coloured squares I and II
area of Ist square = a2 = 42 = 16 sq.units
area of IInd square = b2 = 22 = 4 sq.units
Area of two coloured rectangles III and IV = 2(a x b) = 2(4 x 2) = 16 sq. units
Now, total area of four quadrilaterals (calculated)
= a2 + b2 + 2(ab)
= 16+4+16
= 36 sq. units ……….(ii)
Area of square ABCD = Total area of four quadrilaterals = 36 sq. units
Equating (i) and (ii)
Area of square PQRS = Area of square ABCD
i.e., (a+b)2 = a2 + b2 + 2ab
Result
Algebraic identity (a+b)2 = a2 + 2ab + b2 is verified
Step-by-step explanation:
If I will explain it will take long time.Please mark me as a brainliest answer.
Answer:
Q. 1 Answer:
(a+b)(a+b)
a(a+b)+b(a+b)
a2+ab+ab+b2
a2+b2+2ab
Q. 2 Answer:
the formulas for cube and cuboid are defined based on their surface areas, lateral surface area and volume.
.....
cube and cuboid formula
cube
total surface area
6(side)
cuboid
total surface area
2(l×b+b×h+l×h)