\(a,x^2+2xy+7x+7y+y^2+10\)
\(=\left(x^2+2xy+y^2\right)+\left(7x+7y\right)+10\)
\(=\left(x+y\right)^2+7\left(x+y\right)+10\)
\(=\left(x+y\right)\left(x+y+7\right)+10\)
Đặt \(x+y=t\) ,có :
\(t\left(t+7\right)+10\)
\(=t^2+7t+10\)
\(=t^2+2t+5t+10\)
\(=t\left(t+2\right)+5\left(t+2\right)\)
\(=\left(t+2\right)\left(t+5\right)\)
\(=\left(x+y+2\right)\left(x+y+5\right)\)
\(b,\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)
\(=\left[\left(a+1\right)\left(a+7\right)\right]\left[\left(a+3\right)\left(a+5\right)\right]+15\)
\(=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)
Đặt \(a^2+8a+7=t\) ,có :
\(t\left(t+8\right)+15\)
\(=t^2+8t+15\)
\(=t^2+3t+5t+15\)
\(=t\left(t+3\right)+5\left(t+3\right)\)
\(=\left(t+3\right)\left(t+5\right)\)
\(=\left(a^2+8a+7+3\right)\left(a^2+8a+7+5\right)\)
\(=\left(a^2+8a+10\right)\left(a^2+8a+12\right)\)
\(=\left(a^2+8a+10\right)\left(a^2+6a+2a+12\right)\)
\(=\left(a^2+8a+10\right)\left[a\left(a+6\right)+2\left(a+6\right)\right]\)
\(=\left(a^2+8a+10\right)\left(a+6\right)\left(a+2\right)\)
b
\(A=\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\\ =\left(a+1\right)\left(a+7\right)\left(a+3\right)\left(a+5\right)+15\\ =\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)
Đặt \(a^2+8a+7=t\)
\(\Rightarrow A=t\left(t+8\right)+15\\ =t^2+8t+15\\ =\left(t^2+3t\right)+\left(5t+15\right)\\ =t\left(t+3\right)+5\left(t+3\right)\\ =\left(t+3\right)\left(t+5\right)\\ =\left(a^2+8a+10\right)\left(a^2+8a+12\right)\)
