Question

1) Phân tích:

a)\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)

b)\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)

Answer 1

a)(x+1)(x+2)(x+3)(x+4)+1

=(x+1)(x+4)(x+2)(x+3)+1

=(x²+5x+4)(x²+5x+6)+1

Đặt a=(x²+5x+4) thì (x²+5x+4)(x²+5x+6)+1

= a.(a+2)+1

=a²+2a+1

=(a+1)²

Thay: =(x²+5x+4+1)²

=(x²+5x+5)²

b)(x+2)(x+4)(x+6)(x+8)+16

=(x+2)(x+8)(x+4)(x+6)+16

=(x²+10x+16)(x²+10x+24)+16

Đặt a=(x²+10x+16) thì (x²+10x+16)(x+5x+24)+1

= a.(a+8)+16

=a²+8x+16

=(a+4)²

Thay: =(x²+10x+16+4)²

=(x²+5x+20)²

Answer 2

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Answer 3

a)(x+1)(x+2)(x+3)(x+4)+1

=[(x+1)(x+4][(x+2)(x+3)]+1

=(x2+5x+4)(x2+5x+6)+1

Đặt a=(x2+5x+4)

Ta có: (x2+5x+4)(x2+5x+6)+1

= a.(a+2)+1

=a2+2a+1

=(a+1)2

=(x2+5x+4+1)2

=(x2+5x+5)2

b)(x+2)(x+4)(x+6)(x+8)+16

=(x+2)(x+8)(x+4)(x+6)+16

=(x2+10x+16)(x2+10x+24)+16

Đặt a=(x2+10x+16)

Ta có:(x2+10x+16)(x+5x+24)+1

= a.(a+8)+16

=a2+8x+16

=(a+4)2

=(x2+10x+16+4)2

=(x2+5x+20)2

Mk yêu bé Shin-Conan lém