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a) \(A=\left(3x+2\right)^2-9x\left(x+1\right)\)
\(A=9x^2+12x+4-9x^2-9x\)
\(A=3x+4\)
\(B=\left(2x-1\right)^2-2\left(2x-1\right)\left(5x-1\right)+\left(5x-1\right)^2\)
\(B=\left[2x-1-\left(5x-1\right)\right]^2\)
\(B=\left(2x-1-5x+1\right)^2\)
\(B=\left(-3x\right)^2\)
\(B=9x^2\)
a)\(\left(2x-y\right)[\left(2x\right)^2-2.2x.y+y^2]\)
\(=\left(2x-y\right)^3\)
b)\(2x^2-3xy+5y^2\)
c)\(2x^3-10x^2-11x^2+55x+12x-60\)
\(=2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\)
\(=\left(x+5\right)\left(2x^2-11x+12\right)\)
\(\Leftrightarrow(2x^3-21x^2+67x-60)/\left(x-5\right)=2x^2-11x+12\)
a: \(=\dfrac{\left(x^2-5\right)\left(x^2+5\right)+2x\left(x^2+5\right)}{x^2+5}=x^2+2x-5\)
b: \(=2x^2-2x+3x-3-2x-7\)
\(=2x^2-x-10\)
c: \(=\left(x-y-x-y\right)^2=\left(-2y\right)^2=4y^2\)
d: \(=18x^{2n-3}+3x^n-18x^{2n-3}+2x^n=5x^n\)
giải
a.(2x-3)(4x^2+6x+9)-2x(4x^2-1)
=8x^3+12x^2+18x-12x^2-18x-27-8x^3+2x
=2x-27
bài 1
b.(x+y)2+2(x+y)(x-y)+(x-y)2
= [(x+y)+(x-y)]2
= (x+y-x+y)2
= (2y)2
= 4y2
bài 2
a. 2x2y+4xy+2y
=2y(x2+2x+1)
=2y(x+1)2
b.9x2+6xy-4z2+y2
= (9x2+6xy+y2)-4z2
= (3x+y)2-(2z)2
= (3x+y-2z)(3x+y+2z)
a) (x3 + 8y3) : (2y + x)
= (x + 2y)(x2 - 2xy + 4y2) : (2y + x)
= x2 - 2xy + 4y2
b) (x3 + 3x2y + 3xy2 + y3) : (2x + 2y)
= (x + y)3 : 2(x + y)
= \(\dfrac{\left(x+y\right)^2}{2}\)
c) (6x5y2 - 9x4y3 + 15x3y4) : 3x3y2
= 3x3y2(2x2 - 3xy + 5y2) : 3x3y2
= 2x2 - 3xy + 5y2
\(a,\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)
\(b,\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2=2x^2-3xy+5y^2\)
\(c,\left(2x^3-21x^2+67x-60\right):\left(x-5\right)=\left(2x^3-10x^2-11x^2+55x+12x-60\right):x-5=\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)=\left(x-5\right)\left(2x^2-11x+12\right)\left(x-5\right):\left(x-5\right)=2x^2-11x+12\)
\(B=7x^2-7xy-5x+5y\)
\(=7x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(7x-5\right)\)
\(E=x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
\(F=x^2-9x+18\)
\(=x^2-3x-6x+18\)
\(=x\left(x-3\right)-6\left(x-3\right)\)
\(=\left(x-3\right)\left(x-6\right)\)
\(H=8x^2-2x-1\)
\(=8x^2-4x+2x-1\)
\(=4x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(2x-1\right)\left(4x+1\right)\)
a) \(\left(x+2\right)^2\)
\(=x^2+2\cdot x\cdot2+2^2\)
\(=x^2+4x+4\)
b) \(\left(x-\dfrac{1}{2}\right)^2\)
\(=x^2-2\cdot\dfrac{1}{2}\cdot x+\left(\dfrac{1}{2}\right)^2\)
\(=x^2-x+\dfrac{1}{4}\)
c) \(\left(2x+y\right)\left(2x-y\right)\)
\(=\left(2x\right)^2-y^2\)
\(=4x^2-y^2\)
d) \(9x^2-y^2\)
\(=\left(3x\right)^2-y^2\)
\(=\left(3x+y\right)\left(3x-y\right)\)