Question

phan tich da thuc thanh nhan tu

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

ban nao giai ho mk bai nay voi

mk se tik cho

Answer 1

( x + 2 ) ( x + 3 ) ( x + 4 ) ( x + 5 ) - 24

= ( x² + 7x + 10 ) ( x² + 7x + 12 ) - 24

Đặt x² + 7x + 10 = y

Ta có : 

y² + 2y - 24 = ( y - 4 ) ( y + 6 ) = ( x² + 7x + 6 ) ( x² + 7x + 16 )

                    = ( x + 1 ) ( x + 6 ) ( x² + 7x + 16 )

Answer 2

Đặt x²+7x+10=t

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=t\left(t+2\right)-24=t^2+2t-24\)

\(=\left(t^2+2t+1\right)-25=\left(t+1\right)^2-5^2=\left(t-4\right)\left(t+6\right)\)=(x²+7x+6)(x²+7x+16)

=(x²+x+6x+6)(x²+7x+16)=[x(x+1)+6(x+1)](x²+7x+16)=(x+1)(x+6)(x²+7x+16)

Answer 3

\(B=\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

Đặt:  \(x^2+7x+10=t\)Khi đó B trở thành:

\(B=t\left(t+2\right)-24\)

\(=t^2+2t-24=\left(t-4\right)\left(t+6\right)\)

đến đây bạn thay trở lại