SOLUTION: factor 27f^3+64 2x^3+6x^2+x+3 8m^3-125

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Question 189972: factor
27f^3+64
2x^3+6x^2+x+3
8m^3-125
Answer by cutepiscean5(19) About Me  (Show Source):
You can put this solution on YOUR website!
factor
1.)
+27f%5E3%2B64+
=> +%283f%29%5E3+%2B+%284%29%5E3+
(we will use the formula for +a%5E3+%2B+b%5E3+=+%28a+%2B+b%29%28a%5E2+-+ab+%2B+b%5E2%29+ )
=> +%283f+%2B+4%29%28%283f%29%5E2+-+%283f%29%2A%284%29+%2B+%284%29%5E2%29+
=> +highlight%28%283f+%2B+4%29%289f%5E2+-+12f+%2B+16%29%29+
2.)
+2x%5E3%2B6x%5E2%2Bx%2B3+ (now, we group the first two terms and the last two terms, and take out the common factors from each of them)
=> +2x%5E2%2A%28x%2B3%29+%2B+1%2A%28x%2B3%29+
=> +highlight%28%28x%2B3%29%282x%5E2+%2B+1%29%29+
3.)
+8m%5E3-125+ (this can be expressed as perfect cubes of 2m and 5)
=> +%282m%29%5E3+-+%285%29%5E3+
=> +%282m+-+5%29%28%282m%29%5E2+%2B+%282m%29%2A%285%29+%2B+%285%29%5E2%29+
(we have used the formula for +a%5E3+-+b%5E3+=+%28a+-+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29+ )
=> +highlight%28%282m+-+5%29%284m%5E2+-+10m+%2B+25%29%29+
Hope this helps you.