\(a,a^2\left(a-b\right)+ab\left(a-c\right)=a\left(a+b\right)\left(a-c\right)\\ c,=\left(x^2-2x+1\right)\left(x^2+2x+1\right)=\left(x-1\right)^2\left(x+1\right)^2\\ b,=\left(x-5\right)^2-9y^2=\left(x-5-3y\right)\left(x-5+3y\right)\\ d,=4\left(x^2-9x+14\right)=4\left(x-7\right)\left(x-2\right)\)

Ta có

a 4 + a 3 + a 3 b + a 2 b = a 4 + a 3 + a 3 b + a 2 b = a 3 a + 1 + a 2 b a + 1 = a + 1 a 3 + a 2 b = a + 1 a 2 a + b = a 2 a + b a + 1

Đáp án cần chọn là: A

a) \(45a^3-30a^2+5a-500=5\left(9a^3-6a^2+a-100\right)\)

b) \(a^2b-49b+14b^2-b^3=b\left(a^2-b^2+14b-49\right)=b\left[a^2-\left(b-7\right)^2\right]=b\left(a-b+7\right)\left(a+b-7\right)\)

Tick hộ tui nha 😘

a) $7a^3 - 28a^2 + 28a$

$ = 7a.(a^2 - 4a+4)$

$ = 7a.(a-2)^2$

d) $x^4 + 4$

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

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

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

a) 10x³-90x⁵=10x³(1-9x²)=10x³(1-3x)(1+3x)

b)3a²-6a²b+5a-10ab=(3a²-6a²b)+(5a-10ab)=3a²(1-2b)+5a(1-b)=(3a²+5a)(1-2b)=a(3a+5)(1-2b)

c) 7a³-28a²+28a=7a(a²-4a+4)

d) 45a³-30a²+5a-500=5(9a³-6a²+a-100)

ab(a+b) + bc(b+c) + ca(c+a) = a^2b + ab^2 + b^2c + bc^2 + ca(c+a) + 2abc 
= ab^2 + b^2c + a^2b + bc^2 + 2abc + ca(c+a) 
=b^2(a+c) + b(a^2 + c^2 + 2ac) + ca(c+a) 
=b^2(a+c) + b(a+c)^2 + ca(c+a) 
=(c+a)[b^2 + b(a+c) + ca] 
=(c+a)[b^2 + ab + bc + ca] 
=(c+a)[b(b+a) + c(b+a)] 
=(c+a)(b+c)(b+a)