\(\left(x+2\right)\left(x+3\right)\left(2x-5\right)\left(2x-3\right)-90\)

Rút gọn biểu thức,ta được: \(4x^4+4x^3-41x^2-21x\) (cái này bạn tự làm ở nháp)

Ta có: \(4x^4+4x^3-41x^2-21x\)

\(=4x^4-\left(12x^3-16x^3\right)-\left(48x^2-7x^2\right)-21x\)

\(=4x^4-12x^3+16x^3-48x^2+7x^2-21x\)

\(=4x^3\left(x-3\right)+16x^2\left(x-3\right)+7x\left(x-3\right)\)

\(=\left(x-3\right)\left(4x^3+16x^2+7x\right)\)

\(=\left(x-3\right)\left[4x^3+2x^2+14x^2+7x\right]\)

\(=\left(x-3\right)\left[2x\left(2x^2+x\right)+7\left(2x^2+x\right)\right]\)

\(=\left(x-3\right)\left[\left(2x^2+x\right)\left(2x+7\right)\right]\)

\(=\left(x-3\right)x\left(2x+1\right)\left(2x+7\right)\)

Xong chưa nào??

x(x-4)(x-1)(x+3)+36=[x(x-1)][(x-4)(x+3)]+36

\(=\left(x^2-x\right)\left(x^2-x-12\right)+36\)

Đặt \(t=x^2-x-6\)ta có:

(t+6)(t-6)+36

=t^2 -36 +36

=t^2=....

\(x\left(x-4\right)\left(x-1\right)\left(x+3\right)+36\)

\(=x^4-2x^3-11x^2+12x+36\)

\(=x^4-\left(6x^3-4x^2\right)+\left(9x^2-24x^2+4x^2\right)+\left(36x-24x\right)+36\)

\(=x^4-6x^3+9x^2+4x^3-24x^2+36x+4x^2-24x+36\)

\(=x^2\left(x^2-6x+9\right)+4x\left(x^2-6x+9\right)+4\left(x^2-6x+9\right)\)

\(=\left(x^2-6x+9\right)\left(x^2+4x+4\right)\)

\(=\left(x-3\right)^2\left(x+2\right)^2\)

Xong!

đề là j

(x² -y² +6y -9) : (x-y+3)

= [x²-(y²-6y+9)] : (x-y+3)

=[x²-(y-3)² ] : (x-y+3)

=[(x-y+3)(x+y-3)] :(x-y+3)

=x+y-3