Question

Đã trả lời bởi chuyên gia

Answer 1

a, = ( $a^{2} + b^{2})^{2} - a^{2} b^{2} = (a^{2} + b^{2} - a b) (a^{2} + b^{2} + a b)$

b,

c,= ${(x^{2} + 2)}^{2} - 9 = (x^{2} + 2 - 3) (x^{2} + 2 + 3)$

Answer 2

`a,a ^ 4 + a ^ 2 * b ^ 2 + b ^ 4`$\\$`=a ^ 4 + 2a ^ 2 * b ^ 2 - a ^ 2 * b ^ 2 + b ^ 4`$\\$`=a ^ 4 + 2a ^ 2 * b ^ 2 + b ^ 4 - a ^ 2 * b ^ 2`$\\$`=(a ^ 2 + b ^ 2) ^ 2 - a ^ 2 * b ^ 2`$\\$`=(a ^ 2 + b ^ 2 - ab)(a ^ 2 + b ^ 2 + ab)`$\\$`b,a ^ 8 + a ^ 4 + 1`$\\$`=a ^ 8 + 2a ^ 4 - a ^ 4 + 1`$\\$`=a ^ 8 + 2a ^ 4 + 1 - a ^ 4`$\\$`=(a ^ 4 + 1) ^ 2 - a ^ 4`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + 1 + a ^ 2)`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + a ^ 2 + 1)`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + 2a ^ 2 - a ^ 2 + 1)`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + 2a ^ 2 + 1 - a ^ 2)`$\\$`=(a ^ 4 + 1 - a ^ 2)[(a ^ 2 + 1) ^ 2 - a ^ 2]`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 2 + 1 - a)(a ^ 2 + 1 + a)`$\\$`c,x ^ 4 + 4x ^ 2 - 5`$\\$`=x ^ 4 + 5x ^ 2 - x ^ 2 - 5`$\\$`=x ^ 2 * (x ^ 2 + 5) - (x ^ 2 + 5)`$\\$`=(x ^ 2 + 5)(x ^ 2 - 1)`$\\$`=(x ^ 2 + 5)(x - 1)(x + 1)`$\\$`d,x ^ 3 - 19x - 30`$\\$`=x ^ 3 + 2x ^ 2 - 2x ^ 2 - 4x - 15x - 30`$\\$`=x ^ 2 * (x + 2) - 2x(x + 2) - 15(x + 2)`$\\$`=(x + 2)(x ^ 2 - 2x - 15)`$\\$`=(x + 2)(x ^ 2 + 3x - 5x - 15)`$\\$`=(x + 2)[x(x + 3) - 5(x + 3)]`$\\$`=(x + 2)(x + 3)(x - 5)`

`e`

`ab(a-b)-ac(a+c)+bc(2a+c-b)`

`= a²b-ab²-ac(a+c)+2abc+bc²-b²c`

`= ab(a+c)-b²(a+c)-ac(a+c)+bc(a+c)`

`= (a+c)(ab-b²-ac+bc)`

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

`= (a+c)(b-c)(a-b)`

...Xem thêm

Answer 3

`a,a ^ 4 + a ^ 2 * b ^ 2 + b ^ 4`$\\$`=a ^ 4 + 2a ^ 2 * b ^ 2 - a ^ 2 * b ^ 2 + b ^ 4`$\\$`=a ^ 4 + 2a ^ 2 * b ^ 2 + b ^ 4 - a ^ 2 * b ^ 2`$\\$`=(a ^ 2 + b ^ 2) ^ 2 - a ^ 2 * b ^ 2`$\\$`=(a ^ 2 + b ^ 2 - ab)(a ^ 2 + b ^ 2 + ab)`$\\$`b,a ^ 8 + a ^ 4 + 1`$\\$`=a ^ 8 + 2a ^ 4 - a ^ 4 + 1`$\\$`=a ^ 8 + 2a ^ 4 + 1 - a ^ 4`$\\$`=(a ^ 4 + 1) ^ 2 - a ^ 4`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + 1 + a ^ 2)`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + a ^ 2 + 1)`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + 2a ^ 2 - a ^ 2 + 1)`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 4 + 2a ^ 2 + 1 - a ^ 2)`$\\$`=(a ^ 4 + 1 - a ^ 2)[(a ^ 2 + 1) ^ 2 - a ^ 2]`$\\$`=(a ^ 4 + 1 - a ^ 2)(a ^ 2 + 1 - a)(a ^ 2 + 1 + a)`$\\$`c,x ^ 4 + 4x ^ 2 - 5`$\\$`=x ^ 4 + 5x ^ 2 - x ^ 2 - 5`$\\$`=x ^ 2 * (x ^ 2 + 5) - (x ^ 2 + 5)`$\\$`=(x ^ 2 + 5)(x ^ 2 - 1)`$\\$`=(x ^ 2 + 5)(x - 1)(x + 1)`$\\$`d,x ^ 3 - 19x - 30`$\\$`=x ^ 3 + 2x ^ 2 - 2x ^ 2 - 4x - 15x - 30`$\\$`=x ^ 2 * (x + 2) - 2x(x + 2) - 15(x + 2)`$\\$`=(x + 2)(x ^ 2 - 2x - 15)`$\\$`=(x + 2)(x ^ 2 + 3x - 5x - 15)`$\\$`=(x + 2)[x(x + 3) - 5(x + 3)]`$\\$`=(x + 2)(x + 3)(x - 5)`

`e`

`ab(a-b)-ac(a+c)+bc(2a+c-b)`

`= a²b-ab²-ac(a+c)+2abc+bc²-b²c`

`= ab(a+c)-b²(a+c)-ac(a+c)+bc(a+c)`

`= (a+c)(ab-b²-ac+bc)`

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

`= (a+c)(b-c)(a-b)`

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