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a) 4x3y2 - 8x2y3 + 2x4y
= 2x2y ( 2xy - 4y2 + x2)
= 2x2y (x2 + 2xy + y2 - 5y2)
= 2x2y ( x + y - \(\sqrt{5}\).y)( x + y + \(\sqrt{5}\).y)
b) 2x2y - 4xy2 + 6xy
= 2xy ( x - 2y + 3)
c) - 3x-6xy + 9xz
= -3x( 1 + 2y - 3z)
Ta có : (a + b)(a2 - ab + b2) - 2a(a - b)2
= (a + b).(a - b)2 - 2a(a - b)2
= (a - b)2(a + b - 2a)
a) \(x^3+2x^2-4x+1\)
\(=\left(x^3+3x^2-x\right)-\left(x^2+3x-1\right)\)
\(=x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)
\(=\left(x-1\right)\left(x^2+3x-1\right)\)
c) cho da thuc P(x) =2x^4-7x^3 -2x^2 +13x +6? | Yahoo Hỏi & Đáp
Tham khảo
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
a) 16(4x+5)2 - 25(2x+2)2
\(=\left[4\left(4x+5\right)\right]^2-\left[5\left(2x+2\right)\right]^2\)
\(=\left[4\left(4x+5\right)+5\left(2x+2\right)\right]\left[4\left(4x+5\right)-5\left(2x+2\right)\right]\)
\(=\left(16x+20+10x+10\right)\left(16x+20-10x-10\right)\)
\(=\left(26x+30\right)\left(6x+10\right)\)
\(b,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-2y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-3y+5\right)\)
\(c,\left(x+1\right)^4-\left(x-1\right)^4\)
\(=\left(x+1\right)^{2^2}-\left(x-1\right)^{2^2}\)
\(=\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\)
\(=\left(x^2+2x+1+x^2-2x+1\right)\left[\left(x+1+x-1\right)\left(x+1-x+1\right)\right]\)
\(=\left(2x^2+2\right)2x.2\)
\(=4x.2\left(x^2+1\right)\)
\(=8x\left(x^2+1\right)\)
\(a,x^2-4x+1=0.\)
\(\text{Áp dụng biệt thức }\Delta=b^2-4ac\text{, ta có:}\)(Lớp 9 kì 2 hok)
\(\Delta=-4^2-4.1.1=16-4=12\)
\(\Rightarrow\text{pt có 2 nghiệm }\orbr{\begin{cases}x_1=\frac{4-\sqrt{12}}{2}=2-\sqrt{3}\\x_2=\frac{4+\sqrt{12}}{2}=2+\sqrt{3}\end{cases}}\)
b,bn xem lại đề nếu đúng nói mk 1 tiếng mk làm tiếp cho
1.
a) \(\left(-2x^3\right)\)\(\left(x^2+5x-\frac{1}{2}\right)\) = \(-2x^5\)\(-10x^4\) \(+x^3\)
b) (\(6x^3-7x^2\)\(-x+2\))\(:\left(2x+1\right)\)=\(3x^2-5x+2\)
2.
a) 9x(3x-y) + 3y (y-3x)=9x(3x-y)-3y(3x-y)
= (9x-3y)(3x-y)
= 3(3x-y)(3x-y)
= 3(3x-y)^2
b) \(x^3-3x^2\)\(-9x+27\)= \(\left(x^3-3x^2\right)\)\(-\left(9x-27\right)\)
= \(x^2\left(x-3\right)\)\(-9\left(x-3\right)\)
= \(\left(x^2-9\right)\left(x-3\right)\)
= \(\left(x+3\right)\left(x-3\right)\left(x-3\right)\)
= \(\left(x+3\right)\left(x-3\right)^2\)
Bài 1 ) a ) \(\left(-2x^3\right)\left(x^2+5x-\frac{1}{2}\right)\)
\(=-2x^5-10x^4+x^3\)
b ) \(\left(6x^3-7x^2+x+2\right):\left(2x+1\right)\)
\(=3x^2-5x+2\)
2 ) a ) \(9x\left(3x-y\right)+3y\left(y-3x\right)\)
\(=9x\left(3x-y\right)-3y\left(3x-y\right)\)
\(=\left(3x-y\right)\left(9x-3y\right)\)
\(=3\left(3x-y\right)\left(x-y\right)\)
b ) \(x^3-3x^2-9x+27\)
\(=\left(x^3-3x^2\right)-\left(9x-27\right)\)
\(=x^2\left(x-3\right)-9\left(x-3\right)\)
\(=\left(x^2-9\right)\left(x-3\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x-3\right)\)
a) \(x^8+3x^4+4=x^8+4x^4-x^4+4\)
\(=\left(x^4-2\right)^2-x^4\)
\(=\left(x^4-x^2-2\right)\left(x^4-x^2-2x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+1\right)\left(x^2-1\right)\left(x^2+2\right)\)
\(=\left(x^2-2\right)\left(x^2+1\right)\left(x-1\right)\left(x+1\right)\left(x^2+2\right)\)
a, 3x2 - 8x + 4
= 3x2 - 6x - 2x + 4
= 3x(x - 2) - 2(x - 2)
= (3x - 2)(x - 2)
b, x2 - 4xy + 3y2
= x2 - xy - 3xy + 3y2
= x(x - y) - 3y(x - y)
= (x - 3y)(x - y)
\(a)3x^2-8x+4=3x^2-6x-2x+4=3x\left(x-2\right)-2\left(x-2\right)=\left(3x-2\right)\left(x-2\right)\)
\(b)x^2-4xy+3y^2=x^2-xy-3xy+3y^2=x\left(x-y\right)-3y\left(x-y\right)=\left(x-3y\right)\left(x-y\right)\)
\(c)2x^2+3881x-17505=2x^2+3890x-9x-17505=2x\left(x+1945\right)-9\left(x+1945\right)\)
\(=\left(2x-9\right)\left(x+1945\right)\)