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\(9\left(x-3\right)^2-4\left(x-1\right)^2=\left(3x-9\right)^2-\left(2x-2\right)^2\)
\(=\left[\left(3x-9\right)-\left(2x-2\right)\right]\left[\left(3x-9\right)+\left(2x-2\right)\right]\)
\(=\left(3x-9-2x+2\right)\left(3x-9+2x-2\right)\)
\(=\left(x-7\right)\left(5x-11\right)\)
Phân tích đa thức thành nhân tử
27y2-9(x+y)2=\(9\left(3y^2-\left(x+y\right)^2\right)\)
=\(9\left(\sqrt{3}y+x+y\right)\left(\sqrt{3}y-x-y\right)\)
Rút gọn biểu thức
(2x4-x3+3x2): (-1/3x)
=\(\frac{2x^4-x^3+3x^2}{-\frac{1}{3x}}=3x^3\left(-2x^2+x-3\right)\)
3(x4+x+1)-(x2+x+1)2
=3(x2+x+1)(x2-x+1)-(x2+x+1)2
=(x2+x+1)[3(x2-x+1)-(x2-x+1)
=(x2+x+1)(3x2-3x+3-x2+x-1)
=(x2+x+1)(2x2-2x+2)
=(x2+x+1)2(x2-x+1)
bạn vu cong thien làm sai rồi.
\(x^4+x^2+1=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
chứ không phải là:
\(x^4+x+1=\left(x^2+x+1\right)\left(x^2-x+1\right)\)đâu!
Ta có:\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2=3x^4+3x^2+3-x^4-x^2-1-2x^3-2x-2x^2\)
\(=2x^4-2x^3-2x+2=2x^3\left(x-1\right)-2\left(x-1\right)=2\left(x^3-1\right)\left(x-1\right)\)
\(=2\left(x-1\right)^2\left(x^2+x+1\right)\)
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
\(x^2-9-4\left(x+3\right)\)
\(=\left(x-3\right)\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x+3\right)\left(x-3-4\right)\)
\(=\left(x+3\right)\left(x-7\right)\)
x2 - 9 - 4(x + 3)
= (x2 - 9) - 4(x + 3)
= (x2 - 32) - 4(x + 3)
= (x - 3) (x + 3) - 4(x + 3)
= (x + 3) (x - 3 - 4)
= (x + 3) ( x - 7)
ko bít đúng ko !! 547467474856856856856835675743634634645765876976946426436
\(x^2-9-4\left(x+3\right)\)
\(=\left(x-3\right)\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x+3\right)\left(x-3-4\right)\)
\(=\left(x+3\right)\left(x-7\right)\)
\(x^2-9-4\left(x+3\right)\)
\(=\left(x^2-9\right)-4\left(x+3\right)\)
\(=\left(x^2-3^2\right)-4\left(x+3\right)\)
\(=\left(x-3\right)\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x+3\right)\left(x-3-4\right)\)
\(=\left(x+3\right)\left(x-7\right)\)
\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)
\(=3\left(x^4+x^2+1\right)-\left(x^4+x^2+1+2x^3+2x^2+2x\right)\)
\(=\left(x^4+x^2+1\right)\left(3-2x^3-2x^2-2x\right)\)
\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)
\(=3\left(x^2+x+1\right)\left(x+x^2+x+1\right)\)
\(=3\left(x^2+x+1\right)\left(x^2+2x+1\right)\)
\(=3\left(x^2+x+1\right)\left(x+1\right)^2\)
\(9\left(x-3\right)^2-4\left(x+1\right)^2\)
\(=\left[3\left(x-3\right)-2\left(x+1\right)\right].\left[3\left(x-3\right)+2\left(x+1\right)\right]\)
\(=\left(3x-9-2x-2\right)\left(3x-9+2x+2\right)\)
\(=\left(x-11\right)\left(5x-7\right)\)
\(9\left(x-3\right)^2-4\left(x+1\right)^2\)
\(=3^2\left(x-3\right)^2-2^2\left(x+1\right)^2\)
\(=\left[3\left(x-3\right)\right]^2-\left[2\left(x+1\right)\right]^2\)
\(=\left[3x-9\right]^2-\left[2x+2\right]^2\)
\(=\left[3x-9-2x-2\right].\left[3x-9+2x+2\right]\)
\(=\left(x-11\right)\left(5x-7\right)\)
Chúc bạn học tốt.