phân tích thành nhân tử a) x mũ 4 – 4x ² +4x -1 b) a(b ² – c ²)+b(c ²- a ²) +c(a ² – b ²) c) x mũ 4 +4

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1. Đáp án:

   a, `x^4 – 4x^2 + 4x – 1`

   ` = (x^4 – 1) – (4x^2 – 4x)`

   `= (x^2 – 1)(x^2 + 1) – 4x.(x – 1)`

   `= (x – 1)(x + 1)(x^2 + 1) – 4x(x – 1)`

   `= (x – 1)(x^3 +  x^2 + x + 1 – 4x)`

   `=(x – 1)(x^3 + x^2 – 3x + 1)`

   `= (x – 1)[(x^3 + 2x^2 – x) – (x^2 + 2x – 1)]`

   `= (x – 1)[x.(x^2 + 2x – 1) – (x^2 + 2x – 1)]`

   `=(x – 1)(x – 1)(x^2 + 2x – 1)`

   `= (x – 1)^2 . (x^2 + 2x – 1)`

   b, `a(b^2 – c^2) + b(c^2 – a^2) + c(a^2 – b^2)`

   ` = a(b^2 – c^2) + bc^2 – ba^2 + ca^2 – cb^2`

   ` = a(b^2 – c^2) – (cb^2 – bc^2) – (ba^2 – ca^2)`

   `= a(b – c)(b + c) –  bc.(b – c) – a^2 . (b – c)`

   ` = (b – c)(ab + ac – bc – a^2)`

   `=(b – c)[(ac – bc) – (a^2 – ab)]`

   `=(b – c)[c.(a – b) – a.(a – b)]`

   `=(b – c)(c – a)(a – b)`

   c, `x^4 + 4`

   ` = (x^4 + 4x^2 + 4) – 4x^2`

   `= (x^2 + 2)^2 – (2x)^2`

   `= (x^2 – 2x + 2)(x^2 + 2x + 2)`

   Giải thích các bước giải:

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2. Đáp án:

   a/ $(x-1)^2(x+1+\sqrt{2})(x+1-\sqrt{2})$

   b/ $(a-b)(b-c)(c-a)$

   c/ $(x^2+2+2x)(x^2+2-2x)$

   Giải thích các bước giải:

   a/ $x^4-4x^2+4x-1$

   $=x^4-(4x^2-4x+1)$

   $=x^4-(2x-1)^2$

   $=(x^2-2x+1)(x^2+2x-1)$

   $=(x-1)^2[(x^2+2x+1)-2]$

   $=(x-1)^2[(x+1)^2-2]$

   $=(x-1)^2(x+1+\sqrt{2})(x+1-\sqrt{2})$

   b/ $a(b^2-c^2)+b(c^2-a^2)+c(a^2-b^2)$

   $=ab^2-ac^2+bc^2-a^2b+a^2c-b^2c$

   $=(ab^2-a^2b)-(ac^2-bc^2)+(a^2c-b^2c)$

   $=-ab(a-b)-c^2(a-b)+c(a^2-b^2)$

   $=-ab(a-b)-c^2(a-b)+c(a-b)(a+b)$

   $=(a-b)(-ab-c^2+ac+bc)$

   $=(a-b)[-(ab-ac)+(bc-c^2)]$

   $=(a-b)[-a(b-c)+c(b-c)]$

   $=(a-b)(b-c)(c-a)$

   c/ $x^4+4$

   $=x^4+4x^2+4-4x^2$

   $=(x^2+2)^2-4x^2$

   $=(x^2+2+2x)(x^2+2-2x)$

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