Class 9:
Agebraic Identities..

YELLOW

BLUE

GREEN

Expansion

AIM: to verify the identity (x+a)(x+b)=x²+(a+b)x+ab
and its generalisation like (x+a)(y+b) and 
(ax+b)(cx+d) etc.

Use sliders to set up the required algebraic expressions
These sliders are for coefficients a,b,c,d in (ax+b)(cx+d)
and for changing variables from x to y, and + to - operations. 
Check boxes are given for multiplying term by term and to 
see the final answer

AIM

How to proceed with??

Benny Varghese
PGT Mathematics
JNV Pathanamthitta
Kerala-686511

a = 1 (slider from 1 to 10, step 1)
b = 1 (slider from 0 to 1, step 1)
c = 1 (slider from 0 to 1, step 1)
d = 6 (slider from 1 to 10, step 1)
j = If(b ≟ 1, x, y)
e_2 = 1 (slider from 1 to 10, step 1)
f = 1 (slider from 0 to 1, step 1)
g_2 = 1 (slider from 0 to 1, step 1)
h_2 = 1 (slider from 1 to 10, step 1)
p = If(f ≟ 1, x, y)
text6: "" + e_2 + ""
A = (12, 4)
B = (16, 4)
C = (16, 2)
D = (12, 2)
E = (14, 4)
F = Point(xAxis)
G = Point(xAxis)
H = Point(xAxis)
i = Segment(A, E)
j_1 = Segment(B, E)
k = Segment(E, H)
l = Segment(D, C)
m = Segment(B, F)
n = Segment(G, A)
q = Segment(G, F)
text13: "" + d + ""
text14: "" + h_2 + ""
af = Expand(((a * x^(b)) * y^(1 - b)))
text9: "" + af + ""
rf = Expand(((e_2 * x^(f)) * y^(1 - f)))
text10: "" + rf + ""
o = Expand((af(x, y) * rf(x, y)))
text15: "" + o + ""
r = Expand((d * rf(x, y)))
s = Expand(If[c ≟ 1, r, (-r(x, y))])
text16: "" + s + ""
t_1 = Expand(If[g_2 ≟ 1, (h_2 * af(x, y)), ((-h_2) * af(x, y))])
text17: "" + t_1 + ""
u = If(c ≟ 1, d, (-d))
v = If(g_2 ≟ 1, h_2, (-h_2))
uv: (u * v)
w: (u * v)
text18: "" + w + ""
mf = Expand(af(x, y) + u)
nf = Expand(rf(x, y) + v)
z = Expand((mf(x, y) * nf(x, y)))
text20: "(" + mf + ")(" + nf + ") ="
a_1 = Expand(s(x, y) + t_1(x, y))
text26 = If(w > 0, ("+" * w), ("" * w))
text27 = If(b ≠ f ∧ f ≟ 1 ∧ c ≟ 1 ∨ b ≠ f ∧ b ≟ 1 ∧ g_2 ≟ 1, ("+" * a_1), ("" * a_1))
text28: "" + (LaTeX[o + text27 + text26]) + ""
text21: "" + (LaTeX[z]) + ""
text22: "" + (LaTeX[mf]) + ""
text1: "" + (LaTeX[nf]) + ""
text2 = If(c ≟ 1, "+", "-")
text3 = If(g_2 ≟ 1, "+", "-")
I = (13.64, 3.56)
J = (12.4, 2.32)
K = (13.18, 2.36)
c_1 = Ellipse(I, J, K)
L = (15.68, 1.56)
M = (14.48, 0.36)
N = (15.2, 0.38)
d_1 = Ellipse(L, M, N)
O = (15.48, 3.38)
P = (12.56, 0.48)
Q = (13.5, 0.62)
e_1 = Ellipse(O, P, Q)
R = Point(c_1)
S = (8.12, -2.08)
u_1 = Vector(R, S)
T = Point(e_1)
U = (10.3, -1.94)
v_1 = Vector(T, U)
V = Point(d_1)
W = (12.52, -1.96)
w_1 = Vector(V, W)
text4: "" + o + ""
text5: "" + text27 + ""
text7: "" + text26 + ""
b_1 = false
f_1 = false
g = false
stroke1 = PolyLine((1.7400000000000007, 0.740000000000001), (NaN, NaN), (1.7400000000000007, 0.740000000000001), (1.7800000000000007, 0.680000000000001), (1.8000000000000007, 0.620000000000001), (1.8400000000000007, 0.560000000000001), (1.8600000000000008, 0.48000000000000104), (1.8800000000000008, 0.4200000000000011), (1.9200000000000008, 0.3600000000000011), (1.9400000000000008, 0.3000000000000011), (1.9600000000000009, 0.2400000000000011), (2.020000000000001, 0.1600000000000011), (2.040000000000001, 0.10000000000000112), (2.060000000000001, 0.04000000000000113), (2.100000000000001, -0.039999999999998856), (2.120000000000001, -0.09999999999999885), (2.140000000000001, -0.15999999999999884), (2.180000000000001, -0.21999999999999884), (2.220000000000001, -0.2799999999999988), (2.240000000000001, -0.3599999999999988), (2.280000000000001, -0.4199999999999988), (2.300000000000001, -0.4999999999999988), (2.360000000000001, -0.5399999999999988), (2.3800000000000012, -0.6199999999999988), (2.4200000000000013, -0.6999999999999987), (2.4600000000000013, -0.7599999999999988), (2.4600000000000013, -0.8399999999999987), (2.5200000000000014, -0.8999999999999987), (2.5600000000000014, -0.9599999999999987), (2.5800000000000014, -1.0399999999999987), (2.6200000000000014, -1.0999999999999988), (2.6600000000000015, -1.1599999999999986), (2.7000000000000015, -1.2199999999999986), (2.760000000000002, -1.2799999999999987), (2.800000000000002, -1.3399999999999987), (2.860000000000002, -1.3999999999999986), (2.900000000000002, -1.4599999999999986), (2.960000000000002, -1.4999999999999987), (3.0400000000000023, -1.5799999999999985), (3.1000000000000023, -1.6399999999999986), (3.1600000000000024, -1.6599999999999986), (3.2200000000000024, -1.7199999999999986), (3.2800000000000025, -1.7399999999999987), (3.3400000000000025, -1.7799999999999987), (3.4000000000000026, -1.7999999999999985), (3.4600000000000026, -1.8399999999999985), (3.5600000000000027, -1.9199999999999986), (3.6200000000000028, -1.9399999999999986), (3.680000000000003, -1.9799999999999986), (3.740000000000003, -1.9999999999999987), (3.800000000000003, -2.0199999999999987), (3.860000000000003, -2.0399999999999987), (3.920000000000003, -2.0799999999999987), (3.980000000000003, -2.1199999999999983), (4.040000000000004, -2.1399999999999983), (4.100000000000003, -2.1799999999999984), (4.160000000000004, -2.1999999999999984), (4.220000000000003, -2.2199999999999984), (4.300000000000003, -2.2599999999999985), (4.400000000000004, -2.2799999999999985), (4.4600000000000035, -2.2999999999999985), (4.520000000000004, -2.3199999999999985), (4.580000000000004, -2.3399999999999985), (4.640000000000004, -2.3599999999999985), (4.700000000000004, -2.3799999999999986), (4.780000000000004, -2.4399999999999986), (4.880000000000004, -2.4599999999999986), (4.980000000000004, -2.4799999999999986), (5.060000000000004, -2.5199999999999987), (5.1200000000000045, -2.5399999999999983), (5.200000000000005, -2.5399999999999983), (5.280000000000005, -2.5399999999999983), (5.340000000000004, -2.5799999999999983), (5.440000000000005, -2.5799999999999983), (5.520000000000005, -2.5999999999999983), (5.600000000000005, -2.6199999999999983), (5.700000000000005, -2.6399999999999983), (5.780000000000005, -2.6599999999999984), (5.860000000000005, -2.6599999999999984), (5.960000000000005, -2.6599999999999984), (6.020000000000005, -2.6799999999999984), (6.080000000000005, -2.6999999999999984), (6.1600000000000055, -2.6999999999999984), (6.220000000000005, -2.7199999999999984), (6.300000000000005, -2.7199999999999984), (6.380000000000005, -2.7199999999999984), (6.460000000000005, -2.7199999999999984), (6.520000000000006, -2.7599999999999985), (6.600000000000006, -2.7599999999999985), (6.660000000000006, -2.7399999999999984), (6.740000000000006, -2.7399999999999984), (6.8200000000000065, -2.7399999999999984), (6.900000000000007, -2.7399999999999984), (6.960000000000006, -2.6999999999999984), (7.040000000000006, -2.6799999999999984), (7.120000000000006, -2.6599999999999984), true)
stroke2 = PolyLine((1.6600000000000006, 0.2000000000000011), (NaN, NaN), (1.6600000000000006, 0.2000000000000011), (1.6600000000000006, 0.2800000000000011), (1.6800000000000006, 0.3400000000000011), (1.6800000000000006, 0.4200000000000011), (1.7000000000000006, 0.48000000000000104), (1.7400000000000007, 0.560000000000001), (1.7400000000000007, 0.640000000000001), (1.7600000000000007, 0.7000000000000011), (1.7600000000000007, 0.800000000000001), (1.8400000000000007, 0.780000000000001), (1.8800000000000008, 0.720000000000001), (1.9400000000000008, 0.680000000000001), (2.000000000000001, 0.620000000000001), (2.060000000000001, 0.5800000000000011), (2.120000000000001, 0.560000000000001), (2.180000000000001, 0.5000000000000011), (2.240000000000001, 0.48000000000000104), (2.280000000000001, 0.4200000000000011), (2.340000000000001, 0.38000000000000106), true)
e = false
aim = false
h: false
t: 0