Q. 44.1( 207 Votes )

Expand each of the following, using suitable identities:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Answer :

(i) Using identity,

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Here, a = x, b = 2y and c = 4z


(x + 2y + 4z)2 = x2 + (2y)2 + (4z)2 + (2 × x × 2y) + (2 × 2y × 4z) + (2 × 4z × x)


= x2 + 4y2 + 16z2 + 4xy + 16yz + 8xz


(ii) Using identity,


(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca


Here, a = 2x, b = -y and c = z

(2x – y + z)2 = (2x)2 + (-y)2 + z2 + (2 × 2x × -y) + (2 × -y × z) + (2 × z × 2x)

= 4x2 + y2 + z2 – 4xy – 2yz + 4xz


(iii) Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca


Here, a = -2x, b = 3y and c = 2z

(-2x + 3y + 2z)2 = (-2x)2 + (3y)2 + (2z)2 + (2 × -2x × 3y) + (2 × 3y × 2z) + (2 × 2z × -2x)

= 4x2 + 9y2 + 4z2 – 12xy + 12yz – 8xz


(iv) Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Here, a = 3a, b = -7b and c = -c

(3a – 7b – c)2 = (3a)2 + (-7b)2 + (-c)2+ (2 ×3a × -7b) + (2 × -7b × -c) + (2 × -c × 3a)

= 9a2 + 49b2 + c2 – 42ab + 14bc – 6ac


(v) Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca


Here, a = -2x, b = 5y and c = -3z

(-2x + 5y – 3z)2 = (-2x)2 + (5y)2 + (-3z)2+ (2 ×-2x × 5y) + (2 × 5y × -3z) + (2 × -3z × -2x)

= 4x2 + 25y2 + 9z2 – 20xy -30yz + 12xz


(vi) Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca


Here, a = a, b = b and c = 1


(a – b + 1)2 = (a)2 + (-b)2 + (1)2+ (2 ×a × -b) + (2 × -b × 1) + (2 × 1 × a)


= a2 + b2 + 1 – ab - b + a

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | PolynomialsChamp Quiz | PolynomialsChamp Quiz | Polynomials29 mins
Polynomials - Zero to HeroPolynomials - Zero to HeroPolynomials - Zero to Hero42 mins
Genius Quiz | PolynomialsGenius Quiz | PolynomialsGenius Quiz | Polynomials40 mins
Zeros and Degrees of a PolynomialZeros and Degrees of a PolynomialZeros and Degrees of a Polynomial41 mins
Introduction to PolynomialsIntroduction to PolynomialsIntroduction to Polynomials37 mins
Quiz | Imp. Qs. on Algebraic IdentitiesQuiz | Imp. Qs. on Algebraic IdentitiesQuiz | Imp. Qs. on Algebraic Identities65 mins
Basic understanding of PolynomialsBasic understanding of PolynomialsBasic understanding of Polynomials37 mins
Genius Quiz |  Division of Algebraic ExpressionsGenius Quiz |  Division of Algebraic ExpressionsGenius Quiz | Division of Algebraic Expressions37 mins
Methods to find zeroes of a Polynomial-2Methods to find zeroes of a Polynomial-2Methods to find zeroes of a Polynomial-246 mins
Remainder Theorem and Factor TheoremRemainder Theorem and Factor TheoremRemainder Theorem and Factor Theorem38 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

75×75+2×75×25+25×25 equal to

RD Sharma - Mathematics

If x+ =5, then x2+=

RD Sharma - Mathematics

If a2+ =102, find the value of a-.

RD Sharma - Mathematics

Factorize:

2 – 50x2

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

100 – 9x2

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

10x2 – 9x – 7

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

9x2 + 16y2 + 4z2 –24xy + 16yz – 12xz

RS Aggarwal & V Aggarwal - Mathematics

If a1/3+b1/3 + c1/3 =0, then

RD Sharma - Mathematics

Factorize:

x2 – y2 + 6y – 9

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

RS Aggarwal & V Aggarwal - Mathematics