# Look at this pattern12 + (4 × 2) = 3222 + (4 × 3) = 4232 + (4 × 4) = 52i) Write the next two lines.ii) Explain the general principle using algebra.

i) 42 + (4×5) = 62

52 + (4×6) = 72

ii) General principle,

By observing the pattern we can write a general line as:

x2 + (4× (x+1)) = ( x+2 )2

Now, let us prove this using algebra.

x2 + ( 4× (x+1)) = x2 + 4x + 4

(x+2)2 = x2 + 4x + 4 ……using , (x+y)2 = x2 + 2xy + y2

Cleary, both these terms are equal.

Hence, proved.

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 | Algebric Identities46 mins
Discussion on Algebric Identities48 mins
Algebric Expressions and Identities45 mins
Algebraic Expressions and Identities43 mins
Master Algebraic Identities43 mins
Division of Algebraic Expressions36 mins
Smart Revision | Quiz on Algebraic Expression and Identities44 mins
How to Use Algebraic Identities40 mins
Multiplication of Algebraic Expression40 mins
Genius Quiz | Algebraic Expressions and Identities30 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
view all courses