Math, asked by sumansuravi2009, 19 days ago

Do the following activites with diagrammatic representation (by cutting and pasting method using coloured sheets or graph papers):

a)Verify the area of Trapeziu

b)Verify the area of Rhombus

c) Verify these two Algebraic Identities :

i) ( + ) = + +
ii) ( − ) = − + ?
if your ans. is correct then I'll mark you as brainliest

Answers

Answered by adithya2935

Answer:

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.

Learning Outcome

The identity (a+b)2 = a2 + 2ab + b2 is verified by cutting and pasting of paper. This identity can be verified geometrically by taking other values of a and b.

Activity Time

Divide a square plot into four parts (quadrilaterals) such that two parts have same area and other two are squares.

Viva Voce

Question 1.

What is the degree of polynomial x2 + 4x + 2?

Answer:

Question 2.

Write the simplification of (2x + 1)2.

Answer:

4x2+4x+1.

Question 3.

What is the coefficient of x2 in (3x + 1)2 ?

Answer:

Question 4.

Write (x2 + 1x2 + 2) in square form.

Answer:

(x + 1x)2

Question 5.

Factorize x2 + 10x +25.

Answer:

(x+5)2

Question 6.

Write the product of (7x + 3) (7x + 3).

Answer:

49x2 + 42x + 9.

Question 7.

What do you mean by zeroes of the polynomial ?

Answer:

The values of x for which the given polynomial vanishes.

Question 8.

Is −13 the zero of the polynomial 3x + 1?

Answer:

Yes

Question 9.

If f(y) = y2 – y + 1 find f(1).

Answer:

f(1) = (1)2 – (1) + 1 = 1.

Question 10.

(a + b)2 is binomial or trinomial ?

Answer:

Trinomial.

Multiple Choice Questions

Question 1.

How will you find the value of 1012 by using identity (a + b)2:

(i)(100+1)2

(ii) 1002 + 12

(iii) (100-1)2

(iv) none of these

Question 2.

Which algebraic identity can be used to find the value of 912?

(i) (a+ b)2

(ii) a2 – b2

(iii) a3 + b3

(iv) none of these

Question 3.

Simplify: (2x +y)2 (By using identity only).

(i) 2x2 + y2 + 4x

(ii) 4x2 +y2 + 2xy

(iii) 4x2 +y2 + 4xy

(iv) none of these

Question 4.

Find the factors of x2 + 9y2 + 6xy:

(i) (x+3y)(x+3 y)

(ii) (x-3 y)(x+3 y)

(iii) (x-3y)(x-3y)

(iv) none of these

Question 5.

Write the factors of 25x2 + 20x +4:

(i) (5x + 2) (5x + 2)

(ii) (5x- 4) (4 + 5x)

(iii) (4 + 5x)(4 – 5x)

(iv) none of these

Question 6.

What will be area of a square of side (x + 5) ?

(i) x2 + 25

(ii) (x + 5)2

(iii) x + 52

(iv) none of these

Question 7.

Find the factors of 3 + 2√3 x + x2 ?

(i) (x + √3)2

(ii) x2 + 3

(iii) x + (√3)2

(iv) none of these

Question 8.

The expression 4x2 + 12x + 9 represents an area of square, write the dimensions of a square.

(i) (2x + 3) by (2x + 3)

(it) (2x – 3) by (2x + 3)

(iii) 2x by 3

(iv) none of these

Question 9.

If (a + b)2 = 25, a2 = 4, 2ab = 12, then what will be the value of a and b?

(i) a = -2, b = 3

(ii) a = 2, b = -3

(iii) a = 2, b = 3

(iv) none of these

Question 10.

Write the factors of 169 + 26y + y2

(i) (y – 13)2

(ii) (13 + y)2

(iii) (13 – y)2

(iv) none of these

Answers

(i)

(iii)

(i)

(ii)

(i)

(iii)

(ii)

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