Question

8x cube -27y cube
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4x square - 9y square

Answer 1

the student should not do the FOIL method.  The student should recognize immediately that the product will be a2 − b2.

That is skill in algebra.

And the order of factors never matters:

(a + b)(a − b) = (a − b)(a + b) = a2 − b2.

Problem 1.   Write only final product..

a)  (x + 9)(x − 9) = x2 − 81

b)   (y + z)(y − z) = y2 − z2

c)  (6x − 1)(6x + 1) = 36x2 − 1

d)   (3y + 7)(3y − 7) = 9y2 − 49

e)  (x3 − 8)(x3 + 8) = x6 − 64

f)  (xy + 10)(xy − 10) = x2y2 − 100

g)  (xy2 − z3)(xy2 + z3) = x2y4 − z6

h)  (xn + ym)(xn − ym) = x2n − y2m

Problem 2.   Factor.

a)  x2 − 100  = (x + 10)(x − 10)

b)  y2 − 1 = (y + 1)(y − 1)

c)  1 − 4z2 = (1 + 2z)(1 − 2z)

d)  25m2 − 9n2 = (5m + 3n)(5m − 3n)

e)  x6 − 36 = (x3 + 6)(x3 − 6)

f)  y4 − 144  = (y2 + 12)(y2 − 12)

g)  x8 − y10 = (x4 + y5)(x4 − y5)

h)  x2n − 1 = (xn + 1)(xn − 1)

Problem 3.   Factor completely.

  a)  x4 − y4=(x2 + y2)(x2 − y2)  =(x2 + y2)(x + y)(x − y)  b)  1 − z8=(1 + z4)(1 − z4)  =(1 + z4)(1 + z2)(1 − z2)   =(1 + z4)(1 + z2)(1 + z)(1 − z)

Problem 4.    Completely factor each of the following.  First remove a common factor.  Then factor the difference of two squares.

a)  xy2 − xz2  = x(y2 − z2) = x(y + z)(y −z)

b)  8x2 − 72  = 8(x2 − 9) = 8(x + 3)(x 

Answer 2

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