Chapter 4 – Exploring Algebraic Identities

37 questions · Class 9 Mathematics

1

Observe the two rows of figures below.

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2

Algebra tiles can be used to represent products and find factors.

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3

Try to simplify the following rational expression: 36s2 - 12st + t2/t2 + 2ts - 48s2 = (6s - t)2/(\_ + \_)(\_ + \_) (Hint: Factor t2 + 2ts - 48s2 and simplify the rational…

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4

We have seen that (x + 3)(x + 4) = x2 + 7x + 12.

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5

We already know that x2 - y2 = (x - y)(x + y).

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6

James and Reshma were talking about algebraic identities they learnt in school.

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7

Factor the following algebraic expressions:

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8

Find the following products using identities:

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9

Find values using suitable identities:

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10

Find possible expressions for the length and breadth of each of the following rectangles whose areas are given by the following expressions in square units.

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11

Simplify the following:

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12

If a number plus its reciprocal equals 10/3, find the number.

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13

Find possible expressions for the length, breadth, and heights of each of the following cuboids whose volumes are given by the following expressions in cubic units.

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14

The village playground is shaped as a square of side 40 metres.

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15

If both x - 2 and x - 1/2 are factors of px2 + 5x + r, show that p = r.

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16

A rectangular pool has area 2x2 + 7x + 3 sq.

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17

By factoring the expression, check that n3 - n is always divisible by 6 for all natural numbers n.

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18

Find the values: (A) x3 + y3 - 12xy + 64 when x + y = -4 (B) x3 - 8y3 - 36xy - 216 when x = 2y + 6

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19

If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 - 3abc = -25.

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20

Suppose 7x is split as 2x + 5x; can a similar rectangular arrangement be formed?Consider other possibilities and check. [Page No. 79]

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21

Using the identity (a + b)2 = a2 + 2ab + b2, expand the following:

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22

Find the following squares using one of the above identities.

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23

Find the values of the following using the identity (a - b)2 = a2 - 2ab + b2.

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24

Factor completely: (A) 9x2 + 24xy + 16y2 (B) 4s2 + 20st + 25t2 (C) 49x2 + 28xy + 4y2 (D) 64p2 + 32/3pq + 4/9q2 * (E) 3a2 + 4ab + 4/3b2 * (F) 9/5s2 + 6sv + 5v2 [Page No.

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25

Using the same identity (Q.1.), find the values of the following:

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26

Factor using suitable identities:

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27

Is this an identity?

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28

Expand the following using the identity (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca:

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29

Fill in the blanks to complete the following identities:

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30

Select and use the identity that will help you to find the following products without multiplying directly:

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