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a) \(\left(x^2+2xy+y^2\right):\left(x+y\right)\)
\(=\left(x+y\right)^2:\left(x+y\right)\)
\(=x+y\)
b) \(\left(125x^3+1\right):\left(5x+1\right)\)
\(=\left(5x+1\right)\left(25x^2-5x+1\right):\left(5x+1\right)\)
\(=25x^2-5x+1\)
c) \(\left(x^2-2xy+y^2\right):\left(y-x\right)\)
\(=\left(x-y\right)^2:\left(y-x\right)\)
\(=\left(y-x\right)^2:\left(y-x\right)\)
\(=y-x\)
a ) \(\left(x^2+2xy+y^2\right):\left(x+y\right)\)
\(=\left(x+y\right)^2:\left(x+y\right)\)
\(=\left(x+y\right)\)
b ) \(\left(125x^3+1\right)\left(5x+1\right)\)
\(=\left[\left(5x\right)^3+1\right]:\left(5x+1\right)\)
\(=\left(5x\right)^2-5x+1\)
\(=25x^2-5x+1\)
c ) \(\left(x^2-2xy+y^2\right):\left(y-x\right)\)
\(=\left(x-y\right)^2:\left[-\left(x-y\right)\right]\)
\(=-\left(x-y\right)\)
\(=y-x\)
a) \(\left(x^2+2xy+y^2\right):\left(x+y\right)\\ =\left(x+y\right)^2:\left(x+y\right)\\ =\left(x+y\right)\)
b) \(\left(125x^3+1\right)\left(5x+1\right)\\=\left[\left(5x\right)^3+1\right]:\left(5x+1\right)\\ =\left(5x\right)^2-5x+1 \\ =25x^2-5x+1\)
c) \(\left(x^2-2xy+y^2\right):\left(y-x\right)\\ =\left(x-y\right)^2:\left[-\left(x-y\right)\right]\\ =-\left(x-y\right)\\ =y-x\)
a) =(a-b-c +a-b+c)( a-b-c -a+b-c)
= 2(a-b)(-2c)= -4c(a-b)
làm tặng câu a) thui
\(\left(a-b-c\right)^2-\left(a-b+c\right)^2\)
\(=\left(a-b-c-a+b-c\right)\left(a-b-c+a-b+c\right)\)
\(=\left(-2c\right)\left(-2b+2a\right)\)
\(=2\left(a-b\right)\left(-2c\right)\)
\(=-4c\left(a-b\right)\)
a) câu này dài quá à, mình ngại làm lắm
Áp dụng bđt này: \(a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\)
b)\(\left(1+x+x^2\right)\left(1-x\right)\left(1+x\right)\left(1-x+x^2\right)\)
\(=\left[\left(1+x^2\right)+x\right]\left(1-x^2\right)\left[\left(x^2+1\right)-x\right]\)
\(=\left[\left(1+x^2\right)^2-x^2\right]\left(1-x^2\right)\)
\(=\left(1+2x^2+x^4-x^2\right)\left(1-x^2\right)\)
\(=\left(x^4+x^2+1\right)\left(1-x^2\right)\)
Bài 1: Thực hiện phép tính
a) 3x(2x2 - 5x + 9) = \(6x^3-15x^2+27x\)
b) 5x(x2-xy+1) = \(5x^3-5xy+5x\)
c) -2/3x2y(3xy-x2+y) = \(-2x^3y^2+\dfrac{2}{3}x^4y-\dfrac{2}{3}x^2y^2\)
2) Thực hiện phép tính
a) (5x-2y) (x2-xy+1) = \(5x^3+5x-7y-2x^3y+2xy^2\)
b) (x+3y)(x2-2xy+y) = \(x^3-x^2y+xy+6xy^2+y^2\)
c) (3x-5y) (4x+ 7y) = \(12x^2-xy-35y^2\)
Bài 3: Rút gọn các biểu thức sau(bằng cách khai triển hằng đẳng thức):
a) (x+y)2+(x-y)2
= \(x^2+2xy+y^2+x^2-2xy+y^2\)
= \(\left(x^2+x^2\right)+\left(2xy-2xy\right)+\left(y^2+y^2\right)\)
= \(2x^2+2y^2=2\left(x^2+y^2\right)\)
b) (x+2)(x-2)-(x-3)(x+1)
= \(x^2-4\) - \(\left(x^2-2x-3\right)\)= \(x^2-4-x^2+2x+3\)
= \(\left(x^2-x^2\right)+2x+\left(-4+3\right)\)=\(2x-1\)
c) (x-2)(x+2)-(x-2)2
=>\(x^2-4-\left(x^2-2.x.2+2^2\right)=x^2-4-x^2-4x+4=\left(x^2-x^2\right)+\left(-4+4\right)-4x=-4x\)
d) (2x+y)(4x2-2xy+y2)-(2x-y)(4x2+2xy+y2)
= \(8x^3+y^3-\left(8x^3-y^3\right)\)
= \(8x^3+y^3-8x^3+y^3\)
= \(\left(8x^3-8x^3\right)+\left(y^3+y^3\right)\)= \(2y^3\)
\(a,\left(x+3\right).\left(x^2-3x+9\right)-\left(54+x^3\right)=x^3+27-54-x^3=-27.\)
\(b,8x^3+y^3-8x^3+y^3=2y^3\)
- Viết 7 hằng đẳng thức đáng nhớ :
\(\left(A+B\right)^2=A^2+2AB+B^2\)
\(\left(A-B\right)^2=A^2-2AB+B^2\)
\(A^2-B^2=\left(A-B\right)\left(A+B\right)\)
\(\left(A+B\right)^3=A^3+3A^2B+3AB^2+B^3\)
\(\left(A-B\right)^3=A^3-3A^2B+3AB^2-B^3\)
\(A^3-B^3=\left(A-B\right)\left(A^2+AB+B^2\right)\)
\(A^3+B^3=\left(A+B\right)\left(A^2-AB+B^2\right)\)
- Áp dụng :
\(a,\left(x+2y\right)^2=x^2+4xy+4y^2\)
\(b,\left(\dfrac{5x-1}{2}\right)^2=\dfrac{\left(5x-1\right)^2}{2^2}=\dfrac{25x^2-10x+1}{4}\)
\(c,\left(\dfrac{1}{3x-3}\right)\left(\dfrac{1}{3x+3}\right)=\dfrac{1.1}{\left(3x-3\right)\left(3x+3\right)}=\dfrac{1}{9x^2-9}\)
\(d,\left(2x+3\right)^3=8x^3+36x^2+54x+27\)
\(e,\left(\dfrac{1}{4y-2x}\right)^2=\dfrac{1}{\left(4y-2x\right)^2}=\dfrac{1}{16y^2-16xy+4x^2}\)
\(f,\left(2x-y\right)\left(4x^2+2xy+y^2\right)=\left(2x\right)^3-y^3=8x^3-y^3\)
\(g,\left(x+3\right)\left(x^2-3x+9\right)=x^3+27\)
a) (x^2+2xy+y^2) : (x+y)
=(x+y)2:(x+y)
=x+y
b) (125x^3+1) : (5x+1)
=(5x+1)(25x2-5x+1):(5x+1)
=25x2-5x+1
c) (x^2-2xy+y^2) : (y-x)
=(x-y)2:(y-x)
=-(x-y)2:(x-y)
=-(x-y)
=-x+y
a) (x2 + 2xy + y2) : (x + y);
=(x+y)2:(x+y)
=x+y
b) (125x3 + 1) : (5x + 1);
=(5x+1)(25x2-5x+1):(5x+1)
=25x2-5x+1
c) (x2 – 2xy + y2) : (y – x).
=(x-y)2:(y-x)
=(y-x)2:(y-x)
=y-x