01
Algebra I
(x − y)
y
(x + y)
y
x
Sum of Two Cubes x3 + y3
y
B
A
y3
(x − y)
3
x
C
x
x
y
(x + y)
(x − y)
(x − y)
y
x
x
x
y
Vol of A = (y)(y)(x + y)
Vol of B = (x)(y)(x − y)
Vol of C = (x)(x)(x − y)
Vol of A + B + C = (y)(y)(x + y) + (x)(y)(x − y) + (x)(x)(x − y)
Vol of A + B + C = y2x + y3 + x2y − y2x + x3 − x2y
Grouping
Vol of A + B + C = (y2x + y3) + (x2y + x3) + (− y2x − x2y)
ACTIVE MATHS 4
Vol of A + B + C = y2 (x + y) + x2(y + x) − xy(y + x)
Vol of A + B + C = x3 + y3 = (x + y)(x2 − xy + y2)
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