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Start Animation

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Total Area = a²

Now, the \;  remaining \;  Area \; = \; a²-b²

=(a+b)(a-b)

Class 9- Polynomials-Algebraic \;  Identity

a²-b²=(a+b)(a-b)

-BENNY VARGHESE
PGT MATHEMATICS
JNV PATHANAMTHITTA
KERALA-686511

To visualise the algebraic identity
a²-b²=(a+b)(a-b)

AIM

How to proceed with?

Click the “Start Animation ” button to
 see that the area a²-b² becomes that
 of a familiar fgure viz rectangle !!!

A = (5, -3)
B = (5, -1)
C = (7, -1)
D = (7, -3)
q1, a, b, c, d = Polygon(A, B, C, D)
G = (7, -1)
H = (10, 2)
I = (10, -3)
J = (7, -3)
q3, g, h, i, j = Polygon(G, H, I, J)
K = (10, 2)
L = (7, -1)
M = (5, -1)
N = (5, 2)
q4, k, l, m, n = Polygon(K, L, M, N)
e = 0 (slider from 0 to 12, step 0.01)
α = If(e ≤ 7, (((e - 2) * 18))°)
E = (-1, -3)
A' = Dilate(A, If[0.5 < e < 1.5, 1.5 - e, 0], E)
u = Vector(A, A')
A'_1 = Translate(A, u)
B' = Translate(B, u)
C' = Translate(C, u)
D' = Translate(D, u)
q1', a'_1, b', c', d' = Polygon(A'_1, B', C', D')
F = Midpoint(B', A')
O = Midpoint(B, A)
P = Midpoint(A', D')
Q = Midpoint(A, D)
G' = Rotate(G, If[5.5 < e < 10.5, α, 0], K)
H' = Rotate(H, If[5.5 < e < 10.5, α, 0], K)
I' = Rotate(I, If[5.5 < e < 10.5, α, 0], K)
J' = Rotate(J, If[5.5 < e < 10.5, α, 0], K)
q3', g', h', i', j' = Polygon(G', H', I', J')
G'_1 = Rotate(G, If[2 < e < 7, α, 0], K)
H'_1 = Rotate(H, If[2 < e < 7, α, 0], K)
I'_1 = Rotate(I, If[2 < e < 7, α, 0], K)
J'_1 = Rotate(J, If[2 < e < 7, α, 0], K)
q3'_1, g'_1, h'_1, i'_1, j'_1 = Polygon(G'_1, H'_1, I'_1, J'_1)
S = Midpoint(J'_1, I'_1)
T = (10, -1)
U = (13, 2)
V = (15, 2)
W = (15, -1)
q2, t, u_1, v, w = Polygon(T, U, V, W)
Z = Midpoint(V, W)
R = Midpoint(U, V)
A_1 = Midpoint(G'_1, J'_1)
B_1 = Midpoint(N, M)
T' = Dilate(T, If[7.5 < e < 8.5, 8.5 - e, 0], C)
f = Vector(T, T')
T'_1 = Translate(T, f)
U' = Translate(U, f)
V' = Translate(V, f)
W' = Translate(W, f)
q2', t'_1, u', v', w' = Polygon(T'_1, U', V', W')
C_1 = Midpoint(u')
D_1 = Midpoint(v')
o = true
p: false