a) \(a^4-4a^3+8a^2-16a+16\)
\(=a^4-4a^3+4a^2+4a^2-16a+16\)
\(=\left(a^4-4a^3+4a^2\right)+\left(4a^2-16a+16\right)\)
\(=a^2\left(a^2-4a+4\right)+4\left(a^2-4a+4\right)\)
\(=a^2\left(a^2-2.a.2+2^2\right)+4\left(a^2-2.a.2+2^2\right)\)
\(=a^2\left(a-2\right)^2+4\left(a-2\right)^2\)
\(=\left(a-2\right)^2\left(a^2+4\right)\)
b)
x3-3x2-7x-15
= x3-5x2+2x2-10x+3x-15
= x2(x-5) + 2x(x-5) + 3(x-5)
= (x-5)(x2+2x+3)
NGOÀI CÁCH CỦA BN Nguyễn nam RA MK CÒN CÓ CÁCH KHÁC
a) a4 - 4a3 + 8a2 - 16a + 16
= a4 - 2a3 - 2a3 + 4a2+ 4a2 - 8a - 8a + 16
= (a4 - 2a3) - (2a3 - 4a2) + (4a2 - 8a) - (8a - 16)
= a3(a - 2) - 2a2(a - 2) + 4a(a - 2) - 8(a - 2)
= (a3 - 2a2 + 4a - 8)(a - 2)
= [(a3 - 2a2)+ (4a - 8)](a - 2)
= [a2(a - 2) + 4(a - 2)](a - 2)
= (a2 + 4)(a - 2)(a - 2)
= (a2 + 4)(x - 2)2
b) x3 - 3x2 - 7x - 15
= (x3 - 5x2)+ (2x2 - 10x) + (3x - 15)
= x2(x - 5) + 2x(x - 5) + 3(x - 5)
= (x2 + 2x + 3)(x - 5)
c) x5 - x4 - 10x3 - 38x2 - 51x - 45
= x5 - 5x4 + 4x4 - 20x3 + 10x3 - 50x2 + 12x2 - 60x + 9x - 45
= (x5 - 5x4) + (4x4 - 20x3) + (10x3 - 50x2) + (12x2 - 60x) + (9x - 45)
= x4(x - 5) + 4x3(x - 5) + 10x2(x - 5) + 12x(x - 5) + 9(x - 5)
= (x4 + 4x3 + 10x2 + 12x + 9)(x - 5)
= [(x4 + 4x3 + 4x2) + (6x2 + 12x) + 9](x - 5)
= [(x2 + 2x)2 + 2.(x2 + 2x).3 + 32](x - 5)
= (x2 + 2x + 3)2.(x - 5)
