a)
3в³ - 375 = 3*(в³ - 125) = 3*(в - 5)(в² + 5в + 25),
b)
16m² - 8mn + n² + 12m - 3n = (16m² - 8mn + n²) + (12m - 3n) =
= (4m - n)² + 3*(4m - n) = (4m - n)(4m - n + 3)
c)
x² + y² + 2xy + 2x + 2y + 1 = (x² + y² + 2xy) + (2x + 2y) + 1 =
= (х + у)² + 2*(х + у) + 1 = (х + у)(х + у + 2) + 1
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Answers & Comments
a)
3в³ - 375 = 3*(в³ - 125) = 3*(в - 5)(в² + 5в + 25),
b)
16m² - 8mn + n² + 12m - 3n = (16m² - 8mn + n²) + (12m - 3n) =
= (4m - n)² + 3*(4m - n) = (4m - n)(4m - n + 3)
c)
x² + y² + 2xy + 2x + 2y + 1 = (x² + y² + 2xy) + (2x + 2y) + 1 =
= (х + у)² + 2*(х + у) + 1 = (х + у)(х + у + 2) + 1