a, \(x^2+2xy+y^2-x-y-12\)
\(=\left(x^2+2xy+y^2\right)-\left(x+y\right)-12\)
\(=\left(x+y\right)^2-\left(x+y\right)-12\)
\(=\left(x+y\right)^2+3\left(x+y\right)-4\left(x+y\right)-12\)
\(=\left[\left(x+y\right)^2+3\left(x+y\right)\right]-\left[4\left(x+y\right)+12\right]\)
\(=\left(x+y\right).\left[\left(x+y\right)+3\right]-4.\left[\left(x+y\right)+3\right]\)
\(=\left[\left(x+y\right)+3\right].\left[\left(x+y\right)-4\right]\)
b,B = \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
Đặt \(t=x^2+x+1\Rightarrow t+1=x^2+x+2\)
\(\Rightarrow B=t.\left(t+1\right)-12\)
\(B=t^2+t-12\)
\(B=t^2-3t+4t-12\)
\(B=\left(t^2-3t\right)+\left(4t-12\right)\)
\(B=t.\left(t-3\right)+4.\left(t-3\right)=\left(t-3\right).\left(t-4\right)\)
Mà \(t=x^2+x+1\) nên
\(B=\left(x^2+x+1-3\right).\left(x^2+x+1-4\right)\)
\(B=\left(x^2+x-2\right).\left(x^2+x-3\right)\)
\(B=\left(x^2-x+2x-2\right).\left(x^2+x-3\right)\)
\(B=\left[\left(x^2-x\right)+\left(2x-2\right)\right].\left(x^2+x-3\right)\)
\(B=\left[x.\left(x-1\right)+2.\left(x-1\right)\right].\left(x^2+x-3\right)\)
\(B=\left(x-1\right).\left(x+2\right).\left(x^2+x-3\right)\)
Chúc bạn học tốt!!!
a) (x+y)2 - (x+y) -12
=(x+y)2- 4(x+y) + 3(x+y)-12
=(x+y)(x+y-4) + 3 ( x+y -4)
=(x+y-4)(x+y+3)
b) Đặt x2 +x +1 =y
=y(y+1)-12
=y2 +4y -3y -12
= y(y+4) - 3(y+4)
=(y+4)(y-3)
=(x2+x+5)(x2+x-2)
c) =(x2+7x+10)(x2+7x+12) -24
=t ( t +2) -24
=t2 +6t-4t-24
=t(t+6)- 4(t+6)
=(t+6)(t-4)
=(x2+7x+16)(x2+7x+6)
c,C= \(\left(x+2\right).\left(x+3\right).\left(x+4\right).\left(x+5\right)-24\)
\(=\left[\left(x+2\right).\left(x+5\right)\right].\left[\left(x+3\right).\left(x+4\right)\right]-24\)
\(=\left(x^2+5x+2x+10\right).\left(x^2+4x+3x+12\right)-24\)
\(=\left(x^2+7x+10\right).\left(x^2+7x+12\right)-24\)
Đặt \(t=x^2+7x+10\Rightarrow t+2=x^2+7x+12\)
\(\Rightarrow C=t.\left(t+2\right)-24=t^2+2t-24\)
\(C=t^2-4t+6t-24=\left(t^2-4t\right)+\left(6t-24\right)\)
\(C=t.\left(t-4\right)+6.\left(t-4\right)=\left(t-4\right).\left(t+6\right)\)
Mà \(t=x^2+7x+10\) nên:
\(C=\left(x^2+7x+10-4\right).\left(x^2+7x+10+6\right)\)
\(C=\left(x^2+7x+6\right).\left(x^2+7x+16\right)\)
\(C=\left(x^2+x+6x+6\right).\left(x^2+7x+16\right)\)
\(C=\left[\left(x^2+x\right)+\left(6x+6\right)\right].\left(x^2+7x+16\right)\)
\(C=\left[x.\left(x+1\right)+6.\left(x+1\right)\right].\left(x^2+7x+16\right)\)
\(C=\left(x+1\right).\left(x+6\right).\left(x^2+7x+16\right)\)
Chúc bạn học tốt!!!
