phân tích đa thức thành nhân a> a- √a(a ≥0) b>3 √5-5 √3 c>x ²-3 d>a-b(a,b ≥0) e>a+b+2 √ab(a,b ≥0) f>a √a+b √b(a,b ≥0)

`a) a - sqrta (age0)` $\\$` = sqrta . sqrta - sqrta` $\\$ `=sqrta(sqrta-1)` $\\$` b) 3sqrt5 - 5sqrt3` $\\$ `= sqrt45 - sqrt75` $\\$` = sqrt15(sqrt3-sqrt5)` $\\$ `c) x^2 -3` $\\$` = x^2 - (sqrt3)^2` $\\$` = (x-sqrt3)(x+sqrt3)` $\\$` d)a-b ( a,b ge0)` $\\$` = (sqrta)^2 - (sqrtb)^2` $\\$`= (sqrta-sqrtb)(sqrta+sqrtb)` $\\$ `e) a+b +2sqrt(ab )` `(a,bge0)` $\\$ `= (sqrta)^2 +2sqrt(ab) + (sqrtb)^2` $\\$` = (sqrta+sqrtb)^2` $\\$ `f) asqrta + bsqrtb` ` (a,b ge0)` $\\$` = (sqrta)^3 + (sqrtb)^3` $\\$`= (sqrta+sqrtb)(a-sqrt(ab) +b)`

`a)`

`a - \sqrt{a} (a \ge 0)`

` = \sqrt{a} (\sqrt{a} - 1)`

`b)`

`3 \sqrt{5} - 5 \sqrt{3} `

` = \sqrt{3} . \sqrt{5} . (\sqrt{3} - \sqrt{5})`

`=  \sqrt{15} . (\sqrt{3} - \sqrt{5})`

`c)`

`x^2 - 3`

` = x^2 - (\sqrt{3})^2`

` = (x - \sqrt{3})(x + \sqrt{3})`

`d)`

`a - b (a ; b \ge 0)`

` = (\sqrt{a})^2 - (\sqrt{b})^2`

` = (\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})`

`e)`

`a + b + 2 \sqrt{ab} (a ; b \ge 0)`

` = (\sqrt{a})^2 + (\sqrt{b})^2 + 2 . \sqrt{a}.  \sqrt{b}`

`= (\sqrt{a} + \sqrt{b})^2`

`f)`

`a \sqrt{a} + b \sqrt{b} (a ; b \ge 0)`

` = (\sqrt{a})^3 + (\sqrt{b})^3`

` = (\sqrt{a} + \sqrt{b}) [ (\sqrt{a})^2 + \sqrt{a} . \sqrt{b} + (\sqrt{b})^2]`

`=  (\sqrt{a} + \sqrt{b})(a +  \sqrt{ab} + b)`