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### Grade 7 - Mathematics4.24 Finding the value of (a-b)2 (Geometrical Proof)

#### Find the value of (a-b)2

Suppose AC = AF = A units
AB = AG = b units
\ BC = AC - AB = (a - b) units
GF = AF - AG = (a - b) units
HI = BC = (a - b) units and HE = GE = (a - b) units
\ Area of the square HIDE = HI * HE
= (a - b) * (a - b)
= (a - b)2 sq. units    ..........I
Area of square HIDE = Area of square ACDF - Area of rectangle ACIG - Area of rectangle GHEF
= AC * AF - AC * AG - GH * GF
= a.a - a.b - (a-b).b
= a2 - ab - b(a-b)
= a2 - ab - ab + b2
= a2 - 2ab + b2     ..........II
\ From I and II

Ž (a - b)2 = a2 - 2ab + b2

Directions: Solve the following problems. Also write at least ten examples of your own.
 Q 1: (3x-9)2 = _____?9x2-54x+8181x2-54x+819x2-54x+9 Q 2: (6x-5)2 = _____?36x2-60x+256x2-60x+2536x2+60x+25 Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!

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