NCERT Solutions Class 9 Maths Chapter 4 Exploring Algebraic Identities on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities Exercise Set 4.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 4 — Exercise Set 4.1#

$$(a + b)^2 = a^2 + 2ab + b^2$$

To use the identity, decide what $a$ and $b$ are, then write $a^2$, $2ab$ and $b^2$ one after another.

1. Using the identity $(a + b)^2 = a^2 + 2ab + b^2$, expand the following: #

(i) $(7x + 4y)^2$

Here $a = 7x$ and $b = 4y$. We expand $(7x + 4y)^2$:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities Exercise Set 4.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 4 — Exercise Set 4.2#

$$a^2 + 2ab + b^2 = (a + b)^2$$

$$a^2 - 2ab + b^2 = (a - b)^2$$

To factor a perfect square: find $a$ and $b$ whose squares are the first and last terms, then check that the middle term is $2ab$. If the coefficients are awkward, first take out a common factor, as in Example 7.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities Exercise Set 4.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 4 — Exercise Set 4.3#

$$(a + b)^2 = a^2 + 2ab + b^2$$

$$(a - b)^2 = a^2 - 2ab + b^2$$

$$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$$

1. Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. #

(i) $117^2$

117 splits into three easy parts, $100 + 10 + 7$, so we use the $(a + b + c)^2$ identity. We find $117^2$:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities Exercise Set 4.4

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 4 — Exercise Set 4.4#

$$(x + a)(x + b) = x^2 + (a + b)x + ab$$

$$(a + b)(a - b) = a^2 - b^2$$

To factor $x^2 + px + q$: find two numbers whose sum is $p$ and product is $q$, then split the middle term. For $ax^2 + bx + c$, find two numbers whose sum is $b$ and product is $ac$.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities Exercise Set 4.5

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 4 — Exercise Set 4.5#

To simplify a rational expression: factor the numerator and the denominator completely, then cancel the factors they share (which is allowed because the denominator is not zero).

Identities used in this exercise:

$$(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$$

$$a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$$

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities End-of-Chapter Exercises

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 4 — End-of-Chapter Exercises#

$$(a \pm b)^2 = a^2 \pm 2ab + b^2$$

$$(a + b)(a - b) = a^2 - b^2$$

$$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$$

$$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$$

$$(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$$

$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$