a) \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-15\)
\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-15\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-15\)(1)
Đặt \(x^2+5x+4=t\)
\(\Rightarrow\left(1\right)=t\left(t+2\right)-15=t^2+2t+1-16\)
\(=\left(t+1\right)^2-4^2=\left(t+5\right)\left(t-3\right)\)
\(=\left(x^2+5x+9\right)\left(x^2+5x+1\right)\)
b) \(\left(2x+5\right)^2-\left(x-9\right)^2\)
\(=\left(2x+5+x-9\right)\left(2x+5-x+9\right)\)
\(=\left(3x-4\right)\left(x+14\right)\)
a) (x+1)(x+2)(x+3)(x+4) -15
= (x+1)(x+4)(x+2)(x+3)-15
=(x2+5x+4)(x2+5x+6)-15 (*)
đặt x2+5x+5 = k ( k khác 0 )
thì (*) = (k-1)(k+1)-15
=k2-1-15=k2-16
= (k+4)(k-4)
=(x2+5x+9)(x2+5x+1)
b) (2x+5)2-(x-9)2
=(2x+5+x-9)(2x+5-x+9)
=(3x-4)(x+14)
c) 2x2(x +1) + 4x(x +1); d) 2 x(y - 1) - 2
