Factoring by completing the square (Math17A)

Algebra Level 2

Factor this expression completely.

5 ( x − 2 y ) − 125 ( x − 2 y ) 3 5(x - 2y) - 125(x - 2y)^3

( x + 4 ) 2 \small(x+4)^2 5 ( x − 2 y ) ( 1 + 5 x − 10 y ) ( 1 − 5 x + 10 y ) \small 5(x - 2y)(1+5x-10y)(1-5x+10y) ( 5 x 2 + 6 y 4 ) ( 5 x 2 − 6 y 4 ) \small(5x^2+6y^4)(5x^2-6y^4) 5 ( x − 2 y ) ( 1 + 3 x − 5 y ) ( 1 − 3 x + 5 y ) \small 5(x - 2y)(1+3x-5y)(1-3x+5y)

Alagad Matematika by Alagad Matematika , 23, Philippines

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2 solutions

Shivamani Patil
Aug 16, 2014

Let x − 2 y = a x-2y=a

Therefore expression becomes

5 a − 5 a 3 5a-5a^{3} ........Equation no 1

Now let 5 a = z 5a=z

Therefore eqn. 1 becomes

z − z 3 z-z^{3}

= z ( 1 − z 2 z(1-z^{2}

= z ( 1 − z ) ( 1 + z ) z(1-z)(1+z)

substituting yields

5 z ( 1 − 5 z ) ( 1 + 5 z ) 5z(1-5z)(1+5z)

again substituting yields our answer as

5 ( x − 2 y ) ( 1 + 5 x − 10 y ) ( 1 − 5 x + 10 y ) 5(x-2y)(1+5x-10y)(1-5x+10y)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The solution given by Shivamani Patil is most appropriate Did it in the same way.

A Former Brilliant Member - 6 years, 9 months ago

5(x - 2y)(1-25x^2)-100y^2 5(x - 2y)(1+5x)(1-5x) - (10y)^2 5(x - 2y)(1+5x-10y)(1-5x+10y)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

hi po, bakit po naging 1-25 yan? haha pwede pakiexplain?

Jessa Mae - 6 years, 10 months ago

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typographical error ata. hehe.. nasa book namin yan eh.

Philip John Altubar - 6 years, 10 months ago

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