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a ) \(\left(4x^2-9y^2\right):\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y\right);\left(2x-3y\right)\)
\(=2x+3y\)
b ) \(\left(27x^3-1\right):\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2+3x+1\right):\left(3x-1\right)\)
\(=9x^2+3x+1\)
a) (4x2 – 9y2) : (2x – 3y);
=(2x-3y)(2x+3y):(2x-3y)
=2x+3y
b) (27x3 – 1) : (3x – 1);
=(3x-1)(9x2+3x+1):(3x-1)
=9x2+3x+1
c) (8x3 + 1) : (4x2 – 2x + 1);
=(2x+1)(4x2-2x+1):(4x2-2x+1)
=2x+1
d) (x2 – 3x + xy -3y) : (x + y)
=[x.(x-3)+y.(x-3)]:(x+y)
=(x-3)(x+y):(x+y)
=x-3
a) (4x2 – 9y2) : (2x – 3y);
=(2x-3y)(2x+3y):(2x-3y)
=2x+3y
b) (27x3 – 1) : (3x – 1);
=(3x-1)(9x2+3x+1):(3x-1)
=9x2+3x+1
c) (8x3 + 1) : (4x2 – 2x + 1);
=(2x+1)(4x2-2x+1):(4x2-2x+1)
=2x+1
d) (x2 – 3x + xy -3y) : (x + y)
=[x.(x-3)+y.(x-3)]:(x+y)
=(x-3)(x+y):(x+y)
=x-3
a) ( 4x^2 - 9y^2) : ( 2x- 3y) = ( 2x - 3y)(2x + 3y) : (2x- 3y) = 2x + 3y
b) (27x^3 - 1 ) : (3x- 1) = ( 3x - 1 )(9x^2 + 3x + 1 ) : ( 3x - 1 ) = 9x^2 + 3x+ 1
c) ( 9x^3 + 1 ) : (4x^2 - 2x + 1 ) = ( 2x + 1 )(4x^2 - 2x + 1 ) : (4x^2 - 2x + 1 ) = 2x+ 1
d) ( x^2 - 3x + x y - 3y ) : ( x+ y)
= [ x(x- 3 ) + y ( x - 3 ) ] : ( x+ y)
= ( x+ y)(x- 3 ) : ( x+ y)
=x - 3
a) 2x2.(5x3-4x2y-7xy +1) =10x5-8x4y-14x3y+2x2 b) (5x -2y)(x2 -xy +1) =5x3-5x2y+5x-2x2y+2xy2-2y =5x3-7x2y+2xy2+5x-2y c) (\(\dfrac{1}{2}\)x -1)(2x -3) =x2-\(\dfrac{3}{2}\)x-2x+3 =x2-\(\dfrac{7}{2}\)x+3 d) (x +3y)2 =x2+6xy+9y2 e) (3x -2y)2 =9x2-12xy+4y2 g) (\(\dfrac{1}{4}\)x - 3y)(\(\dfrac{1}{4}\)x +3y) =\(\dfrac{1}{16}\)x2-9y2 f) (2x +3)3 =8x3+36x2+54x+27 h) (3 -2y)3 =27-54y+36y2-8y3
a) \(3y^2\left(2y-1\right)+y-y\left(1-y+y^2\right)-y^2+y \)
= \(6y^3-3y^2+y-y+y^2-y^3-y^2+y\)
= \(5y^3-3y^2+y\)
b)\(25x-4\left(3x-1\right)+\left(5-2x\right)7\)
= \(25x-12x+4+35-14x\)
= \(-x+39\)
c) \(11x-2\left(10x-1\right)-\left(4x-1\right)\left(-2\right)\)
= \(11x-\left(20x-2\right)-\left(-8x+2\right)\)
= \(11x-20x+2+8x-2\)
= \(-x\)
d) \(\left(\frac{1}{2x}\right)3-x\left(1-2x-\frac{1}{8x^2}\right)-x\left(x+\frac{1}{2}\right)\)
= \(\frac{3}{2x}-x+2x^2+\frac{x}{8x^2}-x^2-\frac{x}{2}\)
= \(\left(\frac{3}{2x}+\frac{1}{8x}-\frac{x}{2}\right)+x^2-x\)
= \(\left(\frac{12+1-4x^2}{8x}\right)+x^2-x\)
= \(\frac{13-4x^2}{8x}+\frac{8x^3}{8x}-\frac{8x^2}{8x}\)
= \(\frac{13-4x^2+8x^3-8x^2}{8x}\)
= \(\frac{8x^3-12x^2+13}{8x}\)
= x2 - \(\frac{3}{2}\)+\(\frac{13}{8x}\)
e) \(12\left(2-3x\right)+35x-\left(x+1\right)\left(-5\right)\)
= \(24-36x+35x-\left(-5x-5\right)\)
= \(24-36x+35x+5x+5\)
= 4x + 29
a) (4x2 – 9y2) : (2x – 3y) = [(2x)2 – (3y)2] : (2x – 3y) = 2x + 3y;
b) (27x3 – 1) : (3x – 1) = [(3x)3 – 1] : (3x – 1) = (3x)2 + 3x + 1 = 9x2 + 3x + 1
c) (8x3 + 1) : (4x2 – 2x + 1) = [(2x)3 + 1] : (4x2 – 2x + 1)
= (2x + 1)[(2x)2 – 2x + 1] : (4x2 – 2x + 1)
= (2x + 1)(4x2 – 2x + 1) : (4x2 – 2x + 1) = 2x + 1
d) (x2 – 3x + xy -3y) : (x + y)
= [(x2 + xy) – (3x + 3y)] : (x + y)
= [x(x + y) – 3(x + y)] : (x + y)
= (x + y)(x – 3) : (x + y)
= x – 3.
a) (4x2−9y2):(2x−3y)=[(2x)2−(3y)2]:(2x−3y)(4x2−9y2):(2x−3y)=[(2x)2−(3y)2]:(2x−3y)
=(2x−3y).(2x+3y):(2x−3y)=2x+3y=(2x−3y).(2x+3y):(2x−3y)=2x+3y;
b) (27x3−1):(3x−1)=[(3x)3−13]:(3x−1)(27x3−1):(3x−1)=[(3x)3−13]:(3x−1)
=(3x−1).[(3x)2+3x+1]:(3x−1)=9x2+3x+1=(3x−1).[(3x)2+3x+1]:(3x−1)=9x2+3x+1
c) (8x3+1):(4x2−2x+1)=[(2x)3+13]:(4x2−2x+1)(8x3+1):(4x2−2x+1)=[(2x)3+13]:(4x2−2x+1)
=(2x+1)[(2x)2−2x+1]:(4x2−2x+1)=(2x+1)[(2x)2−2x+1]:(4x2−2x+1)
=(2x+1)(4x2−2x+1):(4x2−2x+1)=2x+1=(2x+1)(4x2−2x+1):(4x2−2x+1)=2x+1
d) (x2−3x+xy−3y):(x+y)(x2−3x+xy−3y):(x+y)
=[(x2+xy)−(3x+3y)]:(x+y)=[x(x+y)−3(x+y)]:(x+y)=(x+y)(x−3):(x+y)=x−3