a. 34^2 + 66^2 + 68 x 66

= 34 x 34 + 66 x 66 + 68 x 66

= 34 x 34 + 66 x (66 + 68)

= 34 x 34 + 66 x 134

= 34 x 34 + 66 x 34 + 66 x 100

= 34 x (34 + 66) + 66 x 100

= 34 x 100 + 66 x 100

= (34 + 66) x 100

= 100 x 100

= 10000

\(34^2+66^2+68.66\)

\(=34.34+66.66+68.66\)

\(=34.34+66.\left(68+66\right)\)

\(=34.34+66.134\)

\(=34.34+66.\left(100+34\right)\)

\(=34.34+66.100+66.34\)

\(=34.\left(66+34\right)+66.100\)

\(=34.100+66.100\)

\(=\left(34+66\right).100\)

\(=100^2\)

\(=10000\)

\(a,\left(2x-y\right)\left(2x+y\right)-\left(2x+y\right)^2\)

\(=4x^2-y^2-4x^2-4xy+y^2\)

\(=-4xy\)

\(b,\left(x-3\right)\left(x^2+3x+9\right)-\left(5-x\right)^2\)

\(=x^3-27-25+10x-x^2\)

\(=x^3-x^2+10x-52\)

\(c,\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x+y\right)^3\)

\(=8x^3+y^3-4x^2-4xy-y^2\)

\(d,\left(3x-5\right)^2-\left(3x+5\right)^2\)

\(=\left(3x-5-3x-5\right)\left(3x-5+3x+5\right)\)

\(=-10.6x=-60x\)

a) (2x-y)(2x+y)-(2x+y)^2 

= 4x²-y²-(4x²+4xy+y²)

=  4x²-y²-4x²-4xy-y²

^{= -4xy}

b) (x-3)(x^2+3x+9)-(5-x)^2 

= (x³-27)-(25-10x+x²)

= x³-27-25+10x-x²

= x³-x²+10x-52

c) (2x+y)(4x^2-2xy+y^2)-(2x+y)^3   

= (2x)³+y³- ((2x)³+3.4x².y+3.y².2x+y³)

= 8x³+y³-(8x³+12x²y+6xy²+y³)

= 8x³+y³-(8x³+12x²y+6xy²+y³)

= 8x³+y³-8x³-12x²y-6xy²-y³

⁼-12x²y-6xy²

 d) (3x-5)^2-(3x+5)^2

= (3x-5-3x-5)(3x-5+3x+5)

= -10.6x

= -60x 

a) \(\left(2+xy\right)^2=x^2y^2+4xy+4\)

b) \(\left(5-x^2\right)\left(5+x^2\right)=25-x^4\)

d) \(\left(x+3\right)\left(x^2-3x+9\right)=x^3+27\)

e) \(\left(5-3x\right)^2=9x^2-30x+25\)

f) \(\left(5x-1\right)^3=125x^3-75x^2+15x-1\)

a) (x+3)(x^2-3x+9)-(54+x^3)

= x^3- 3x^2+9x+3x^2-9x+27-54-x63

= -27

b) (2x + y)(4x^2 – 2xy + y^2) – (2x – y)(4x^2+ 2xy + y^2)

= (2x + y)[(2x)^2 – 2x.y + y^2] – (2x – y)[(2x)^2 + 2x.y + y^2]

= [(2x)3^3+ y^3] – [(2x)^3 – y^3]

= (2x)^3 + y^3 – (2x)^3 + y^3

= 2y^3

a)(x+3)(X^2-3x+9)-(54+x^3)

= \(x^3\)+ \(3^3 \) - 54 -\(x^3\)

= 27- 54

= -27

b)(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)

= \((2x)^3\) + \(y^3\)  - [\((2x)^3\) - \(y^3\) ]

= \(8x^3\) + \(y^3\) - \(8x^3\) + \(y^3\)

= \(2y^3\)

a) Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)

\(=x^3+27-54-x^3\)

=-27

a) ( x + 2 )( x² - 2x + 4 ) - ( 18 + x³ )

= x³ + 8 - 18 - x³ = -10

b) ( 2x - y )( 4x² + 2xy + y² ) - ( 2x + y )( 4x² - 2xy + y² )

= 8x³ - y³ - ( 8x³ + y³ )

= 8x³ - y³ - 8x³ - y³ = -2y³

c) ( x - 3 )( x + 3 ) - ( x + 5 )( x - 1 )

= x² - 9 - ( x² + 4x - 5 )

= x² - 9 - x² - 4x + 5 = -4x - 4

d) ( 3x - 2 )² + ( x + 1 )² + 2( 3x - 2 )( x + 1 )

= ( 3x - 2 + x + 1 )² 

= ( 4x - 1 )² 

1) \(5x-5y+x\left(x-y\right)\)

\(=5\left(x-y\right)+x\left(x-y\right)\)

\(=\left(x-y\right)\left(x+5\right)\)

2) \(x^2+4x+3\)

\(=\left(x^2+x\right)+\left(3x+3\right)\)

\(=x\left(x+1\right)+3\left(x+1\right)\)

\(=\left(x+1\right)\left(x+3\right)\)

3) \(x^2-2xy+y^2-z^2\)

\(=\left(x-y\right)^2-z^2\)

\(=\left(x-y-z\right)\left(x-y+z\right)\)

4) \(x\left(x-5\right)-3x+15\)

\(=x\left(x-5\right)-3\left(x-5\right)\)

\(=\left(x-5\right)\left(x-3\right)\)

5) \(y^2-x^2+2x-1\)

\(=y^2-\left(x^2-2x+1\right)\)

\(=y^2-\left(x-1\right)^2\)

\(=\left(x+y-1\right)\left(y-x+1\right)\)

\(1.\left(x-y\right)\left(x+5\right)\)

\(2.\left(x+1\right)\left(x+3\right)\)

\(3.\left(x-y-z\right)\left(x-y+z\right)\)

\(4.\left(x-3\right)\left(x-5\right)\)

\(5.\left(y-x+1\right)\left(y+x+1\right)\)

\(7.\left(x+1\right)\left(x-2\right)^2\)

\(8.\left(x-5\right)\left(x+3\right)\)

\(10.\left(y+1\right)\left(2x+z\right)\)

1)

5x - 5y + x ( x - y ) = (x-y)(5+x)

2)

x²+4x+3=x²+x+3x+3=(x+1)(x+3)

3)x²-2xy+y²-z²=\(\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

4)\(x\left(x-5\right)-3x+15=\left(x-3\right)\left(x-5\right)\)

tt thôi nha dài lắmTruong minh quan cái này dễ mà cũng hỏi