(A+B)(A-B) = A²-B²
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Answers
Answer:
Here is your answer.
Step-by-step explanation:
Objective
To verify the identity a2 – b2 = (a + b)(a – b) by paper cutting and pasting.
Prerequisite Knowledge
1) Area of square = a2, where side of a square = a.
2) Area of rectangle = l x b.
Materials Required
White sheets of paper, two glazed papers (pink and blue), a pair of scissors, geometry box, glues tick.
Procedure
Take any two distinct values of a and b (a > b) say a = 5 units, b = 3 units.
1) Draw a pink square of side 5 units and name it as ABCD as shown in fig.1
2) Draw a blue square of side 3 units and name it as EFGH as shown in fig 2
3) Cut these squares from glazed papers.
4) Paste two squares on a white sheet of paper. Square EFGH is pasted over square ABCD as shown in fig. (iii).
5) Join FC. Cut the pink portion along FC and dotted lines. We get two quadrilaterals as EFCB and GFCD.
6) Now, place these two quadrilaterals on other white sheet of paper such that we get a rectangle. One piece of quadrilateral is reversed to other as shown in fig.(iv) and fig.(v).
Observation and Calculation
In fig. (i), area of square ABCD = a2 = (5)2 = 25 sq. units
fig. (ii), area of square EFGH = b2 = (3)2 = 9 sq. units
fig. (iii), area of quadrilateral EBCF + area of quadrilateral GFCD = area of ABCD – area of square EFGH
= (a2 – b2) sq. units
= 25 – 9
= 16 sq. units … (i)
fig. (v), area of rectangle EDGB = EB x ED
= (a – b)(a+b)
= (5 – 3)(5 + 3)
= 2 x 8
= 16 sq. units … (ii)
From (i) and (ii), we have a2 – b2 = (a – b)(a + b)
Result
The identity (a2 – b2) = (a + b) (a – b) is verified by paper cutting and pasting.
Hope you liked this way of verification!
Answer:
LHS:-
(A+B)(A-B)=
A(A-B)+B(A-B)
A×A-B×A + B×A-B×B
A²- BA + BA- B²
( IN THE NEXT STEP -BA AND +BA GETS CANCELLED, THEREFORE)
A²-B²
THEREFORE
LHS=RHS
hence its proved!!
I hope this solution of mine will help uu.