Question

[nguyễn ngọc minh ánh]

( x mũ 2 + 8x + 7 ) ( x mũ 2 + 8x + 15 )+ 15

Answer 1

[Thành Sherlocks Holmes]

\(\left(x^2+8x+7\right)\cdot\left(x^2+8x+15\right)+15=\left(x^2+8x+11\right)^2-16+15\)

    \(\left(x^2+8x+11\right)^2-1=\left(x^2+8x+10\right)\cdot\left(x^2+8x+12\right)=\left(x^2+8x+10\right)\cdot\left(x+2\right)\cdot\left(x+6\right)\)

Answer 2

[l҉o҉n҉g҉ d҉z҉]

( x² + 8x + 7 )( x² + 8x + 15 ) + 15 (1)

Đặt t = x² + 8x + 7 

(1) <=> t( t + 8 ) + 15

       = t² + 8t + 15

       = t² + 3t + 5t + 15

       = t( t + 3 ) + 5( t + 3 )

       = ( t + 3 )( t + 5 )

       = ( x² + 8x + 7 + 3 )( x² + 8x + 7 + 5 )

       = ( x² + 8x + 10 )( x² + 8x + 12 )

       = ( x² + 8x + 10 )( x² + 2x + 6x + 12 )

       = ( x² + 8x + 10 )[ x( x + 2 ) + 6( x + 2 ) ]

       = ( x² + 8x + 10 )( x + 2 )( x + 6 )