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\(=6x^2+9x+4x+6\)
\(=3x.\left(2x+3\right)+2.\left(2x+3\right)\)
\(=\left(2x+3\right).\left(3x+2\right)\)
\(\)
x2-y2+6x+6y = (x2-y2)+(6x+6y) = (x-y)(x+y)+6(x+y) = (x-y-6)(x+y)
\(x^2-4x+3\)
\(=x^2-x-3x+3\)
\(=x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(x-3\right)\)
\(9x^2+6x-4y^2+4y=\left(9x^2+6x+1\right)-\left(4y^2-4y+1\right)=\left(3x+1\right)^2-\left(2y-1\right)^2=\left(3x+1-2y+1\right)\left(3x+1+2y-1\right)\)
\(A=\left(x+1\right)\left(x-4\right)\left(x+2\right)\left(x-8\right)+4x^2\)
\(A=\left[\left(x+1\right)\left(x-8\right)\right]\left[\left(x-4\right)\left(x+2\right)\right]+4x^2\)
\(A=\left(x^2-7x-8\right)\left(x^2-2x-8\right)+4x^2\)
Đặt \(p=x^2-4,5x-8\)ta có :
\(A=\left(p-2,5x\right)\left(p+2,5x\right)+4x^2\)
\(A=p^2-\left(2,5x\right)^2+4x^2\)
\(A=p^2-6,25x^2+4x^2\)
\(A=p^2-2,25x^2\)
\(A=p^2-\left(1,5x\right)^2\)
\(A=\left(p-1,5x\right)\left(p+1,5x\right)\)
Thay \(p=x^2-4,5x-8\)vào A ta có :
\(A=\left(x^2-4,5x-8-1,5x\right)\left(x^2-4,5x-8+1,5x\right)\)
\(A=\left(x^2-6x-8\right)\left(x^2-3x-8\right)\)
\(\left(x+1\right)\left(x-4\right)\left(x+2\right)\left(x-8\right)+4x^2\)
\(=\left(x+1\right)\left(x-8\right)\left(x-4\right)\left(x+2\right)+4x^2\)
\(=\left(x^2-7x-8\right)\left(x^2-2x-8\right)+4x^2\)
Đặt \(x^2-2x-8=t\)
Ta có : \(\left(t-5x\right)t+4x^2\)
\(=t^2-5xt+4x^2\)
\(=t^2-2.\frac{5}{2}xt+\frac{25}{4}x^2-\frac{9}{4}x^2\)
\(=\left(t-\frac{5}{2}\right)^2-\frac{9}{4}x^2\)
\(=\left(t-\frac{5}{2}-\frac{3}{2}x\right)\left(t-\frac{5}{2}+\frac{3}{2}x\right)\)
Học tốt ~~
\(=\left(x^2+4x-3\right)^2-5\left(x^2+4x-3\right)+6x^2\)
\(=x^4+16x^2+9+8x^3-24x-6x^2-5x^2-20x+15+6x^2\)
\(=x^4+8x^3+11x^2-44x+24\)
\(=\left(x^4-x^3\right)+\left(9x^3-9x^2\right)+\left(20x^2-20x\right)-\left(24x-24\right)\)
\(=x^3\left(x-1\right)+9x^2\left(x-1\right)+20x\left(x-1\right)-24\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+9x^2+20x-24\right)\)
\(4\left(x+3y-4\right)^2-x^2+6x-9\)
\(=\left[2\left(x+3y-4\right)\right]^2-\left(x^2-6x+9\right)\)
\(=\left[2x+6y-8\right]^2-\left(x-3\right)^2\)
\(=\left(2x+6y-8+x-3\right)\left(2x+6y-8-x+3\right)\)
\(=\left(3x+6y-11\right)\left(x+6y-5\right)\)
\(\left(2x^2\right)^2+2.2x^2.9+81-\left(6x\right)^2=\left(2x^2+9\right)-\left(6x\right)^2=\left(2x^2+6x+9\right)\left(2x^2-6x+9\right)\)
bài này 1h rùi,chắc chờ tui ngủ dậy làm;
= (x+y)3 - (x+y) + xy(x+y) =
= (x+y)((x+y)2 -1 +xy)) = (x+y)(x2 +3xy +y2 -1)
4x+5xy-6x+9x2=9x2-2x+5xy=x(9x-2+5y)
hình như đề sai rồi
bài dung mà