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A= \(x.\left\{\left[x.\left(x^2-7\right)\right]^2-6^2\right\}=x.\left[x.\left(x^2-7\right)-6\right].\left[x.\left(x^2-7\right)+6\right]\)
A=\(x.\left[x^3-7x-6\right].\left[x^3-7x+6\right]\)
A= \(x.\left(x-3\right).\left(x+1\right).\left(x+2\right).\left(x+3\right).\left(x-1\right).\left(x-2\right)\)
=(x2-y2)-(x+y)
=(x-y)(x+y)-(x+y)
=(x+y)[(x-y)-1]
=(x+y)(x-y-1)
x^7+x^2+2
=(x^7+x^6+x^5)-(x^6+x^5+x^4)+(x^4+x^3+x^2) +(1 -x^3)
=x^5(x^2+1)-x^4(x^2+1)+x^2(x^2+1)+(1-x)(1+x+x^2)
=(x^2+1)(x^5-x^4+x^2-x+1)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
\(9\left(x-5\right)^2-\left(x+7\right)^2\)
\(=\)\(3^2\left(x-5\right)^2-\left(x+7\right)^2\)
\(=\)\(\left[3\left(x-5\right)\right]^2-\left(x+7\right)^2\)
\(=\)\(\left(3x-15\right)^2-\left(x+7\right)^2\)
\(=\)\(\left(3x-15-x-7\right)\left(3x-15+x+7\right)\)
\(=\)\(\left(2x-22\right)\left(4x-8\right)\)
\(=\)\(2\left(x-11\right).4\left(x-2\right)\)
\(=\)\(8\left(x-11\right)\left(x-2\right)\)
Chúc bạn học tốt ~
\(a,x^2\left(1-x^2\right)-4-4x^2\)
\(=x^2-x^4-4-4x^2\)
\(=x^2-\left(x^4+4x^2+4\right)\)
\(=x^2-\left(x^2+2\right)^2\)
\(=\left(2x^2+2\right).\left(-2\right)\)
\(=-4\left(x^2+1\right)\)
\(A=\left(x^2+3x+1\right)\left(x^2+3x-3\right)-5\)
Đặt \(t=x^2+3x+1\) thì A thành
\(t\left(t-4\right)-5=t^2-4t-5\)
\(t^2-5t+t-5=t\left(t-5\right)+\left(t-5\right)\)
\(=\left(t-5\right)\left(t+1\right)=\left(x^2+3x+1-5\right)\left(x^2+3x+1+1\right)\)
\(=\left(x^2+3x-4\right)\left(x^2+3x+2\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+2\right)\left(x+4\right)\)
\(x^2-x-2017.2018\)
\(=x^2-2018x+2017x-2017.2018\)
\(=x.\left(x-2018\right)+2017.\left(x-2018\right)\)
\(=\left(x-2018\right).\left(x+2017\right)\)
Mơn nhìu