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Algebraic Identity - Square of difference of Binomial

Algebraic Identities - Concepts

Algebraic Identity - Square of Sum of Binomial

Algebraic Identity - Square of difference of Binomial

Algebraic Identity - Dfference of Square

Algebraic Identity -3

Algebraic Identity - Square of Trinomial

Class - 8th DAV Subjects

Concept Explanation

Algebraic Identity - Square of difference of Binomial

Algebraic Identity - Square of Difference of Binomial : -

$small (a-b)^{2}=a^{2}-2ab+b^{2}$

You can easily get this identity by multiplying binomial a-b with itself,

$small (a-b)^{2}=(a-b)(a-b)$

$small = a(a-b)-b(a-b)$

$small = a^2-ab-ba+b^{2}$

$small =a^{2}-2ab+b^{^{2}}$

Similarly , $small (b-a)^{2}$ can also be found.

$small (b-a)^{2}=b^{2}-2ba+a^{2}$

$small =a^{2}-2ab+b^{2}$

$small (b-a)^{2}=(a-b)^{2}$

Identity -II can also be considered as a special case of identity I when'b' is replaced by '-b'.

Identity -I is :

$small (a+b)^{2}=a^{2}+2ab +b^{2}$

Replace 'b' by ' -b'in the above identity :

$small (a+(-b)^{2})=a^{^{2}}+2atimes (-b)+(-b^{2})$

$small (a-b^{2})=a^{2}-2ab+b^{2}$ which is identity -II.

Example:- Find $small (2x-3y)^{2}$ using identity -II .

Solution: $small (2x-3y)^{2}=(2x)^{2}-2times 2xtimes 3y+(3y)^{2}$

$small = 4x^{2}-12xy +9y^{2}$

Example: Evaluate $small (99)^{2}$ using identity -II.

Solution: $small (99)^{2}=(100-1)^2=100^{2}-2times 100times 1+1$

$small =$ 10000 -200 +1 =9801

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Find the value of $large 97^2$
A. 10609	B. 10209	C. 9609	D. 9409
Right Option : D
View Explanation

Question : 2

Evaluate $large (100-3)^{2}$
A. 9680	B. 9469	C. 9409	D. 9540
Right Option : C
View Explanation

Question : 3

Evaluate: $(93)^2$
A. 90900	B. 50987	C. 8649	D. 77788
Right Option : C
View Explanation

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Chapters

Exponents And Radicals II

Direct and Inverse Variation III

Construction of Quadriletrals

Understanding Quadriletrals II

Understanding Quadriletrals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Mensuration I

Exponents And Radicals I

Direct and Inverse Variation II

Direct and Inverse Variation I

Statistics and Probability I

Statistics and Probability II

Factorisation

Algebraic Identities

Polynomial

Simple and Compound Interest

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Percentages

Introduction to Graphs

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