Question

Giúp mình với.

1. Phân tích thành nhân tử

a)  a² (b+c)+ b² (c-a)+c²(a-b)

b) a³+4a²-29a+24

c) (x+1)(x+3)(x+5)(x+7)+15

Answer 1

a) \(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)\)

\(=a^2\left(b-c\right)+b^2\left[\left(c-b\right)-\left(a-b\right)\right]+c^2\left(a-b\right)\)

\(=a^2\left(b-c\right)-b^2\left(b-c\right)-b^2\left(a-b\right)+c^2\left(a-b\right)\)

\(=\left(b-c\right)\left(a^2-b^2\right)-\left(a-b\right)\left(b^2-c^2\right)\)

\(=\left(b-c\right)\left(a-b\right)\left(a+b\right)-\left(a-b\right)\left(b-c\right)\left(b+c\right)\)

\(=\left(b-c\right)\left(a-b\right)\left(a+b-b-c\right)\)

\(=\left(b-c\right)\left(a-b\right)\left(a-c\right)\)

Answer 2

c) \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)

\(=\left(x+1\right)\left(x+7\right)\left(x+3\right)\left(x+5\right)+15\)

\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\left(1\right)\)

Đặt \(x^2+8x+11=y\)Thay vào (1) ta được 

\(\left(y-4\right)\left(y+4\right)+15\)

\(=y^2-16+15\)

\(=y^2-1\)

\(=\left(y-1\right)\left(y+1\right)\)

\(=\left(x^2+8x+10\right)\left(x^2+8x+11\right)\)

Answer 3

nhầm dong cuối là 

\(\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)