` a) ` ` 4x^2 + 4x - 9y^2 - 6y `
` = 4x^2 + 4x + 1 - (9y^2 + 6y + 1) `
` = (2x + 1)^2 - (3y + 1)^2 `
` = (2x + 1 - 3y - 1)(2x + 1 + 3y + 1) `
` = (2x - 3y)(2x + 3y + 2) `
` b) ` ` x^5 + x^4 + 1 `
` = x^5 - x^2 + x^4 + x^2 + 1 `
` = x^2 (x^3 - 1) + (x^4 + 2x^2 + 1 - x^2) `
` = x^2 (x - 1)(x^2 + x + 1) + [(x^2 + 1)^2 - x^2] `
` = x^2 (x - 1)(x^2 + x + 1) + (x^2 + 1 - x)(x^2 + 1 + x) `
` = (x^2 + x + 1)[x^2 (x - 1) + x^2 + 1 - x] `
` = (x^2 + x + 1)(x^3 - x^2 + x^2 - x + 1) `
` = (x^2 + x + 1)(x^3 - x + 1) `
` c) ` ` (x^2 - 2y)^2 - 4x^2 + 8y - 12 `
` = (x^2 - 2y)^2 - 4(x^2 - 2y) - 12 `
` = (x^2 - 2y)^2 - 6(x^2 - 2y) + 2(x^2 - 2y) - 12 `
` = (x^2 - 2y)(x^2 - 2y - 6) + 2(x^2 - 2y + 6) `
` = (x^2 - 2y + 6)(x^2 - 2y + 2) `
` d) ` ` x(x + 3)(x + 6)(x + 9) + 45 `
` = [x(x + 9)].[(x + 3)(x + 6)] + 45 `
` = (x^2 + 9x)(x^2 + 9x + 18) + 45 `
Đặt ` t = x^2 + 9x ` nên ta có:
` t(t + 18) + 45 `
` = t^2 + 18t + 45 `
` = t^2 + 3t + 15t + 45 `
` = t(t + 3) + 15(t + 3) `
` = (t + 3)(t + 15) `
` = (x^2 + 9x + 3)(x^2 + 9x + 15) `
