( 2x - 3y )² = 4x² - 12xy + 9y²

( 3√x - y )² = 9x - 6y√x + y² ( x ≥ 0 )

\(a)\)

\(4x^2-4x+1\)\(=\left(2x-1\right)^2\)

\(b)\)

\(\left(3x+2\right)\left(2-3x\right)\)\(=4-9x^2\)

\(c)\)

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

\(a,4x^2-4x+1=\left(2x\right)^2-2.2x.1+1=\left(2x-1\right)^2\)

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

\(c,\left(x-3\right)\left(x^2+3x+9\right)=\left(x-3\right)\left(x^2+3x.1+3^2\right)=x^3-3^3\)

Trả lời:

a, 4x² - 4x + 1 = ( 2x )² - 2.2x.1 + 1² = ( 2x - 1 )²

b, ( 3x + 2 ) ( 2 - 3x ) = ( 2 + 3x ) ( 2 - 3x ) = 2² - ( 3x )² = 4 - 9x²

c, ( x - 3 ) ( x² + 3x + 9 ) = ( x - 3 ) ( x² + x.3 + 3² ) = x³ - 3³ = x³ - 27

\(\frac{4}{9}x^2-\frac{2}{3}xy+\frac{1}{4}y^2\)

\(=\left(\frac{2}{3}x\right)^2-2.\frac{2}{3}x.\frac{1}{2}y+\left(\frac{1}{2}y\right)^2\)

\(=\left(\frac{2}{3}x-\frac{1}{2}y\right)^2\)

p/s: chúc bạn học tốt

a) \(\left(x-3\right)^2+2\left(x-3\right)\left(x+2\right)+\left(x+2\right)^2\)

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

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

Hằng đẳng thức: \(\left(a+b\right)^2=a^2+2ab+b^2\).

b) \(\left(x+5\right)^2-\left(2x+10\right)\left(x-6\right)+\left(x-6\right)^2\)

\(=\left(x+5\right)^2-2\left(x+5\right)\left(x-6\right)+\left(x-6\right)^2\)

\(=\left[\left(x+5\right)-\left(x-6\right)\right]^2\)

\(=11^2=121\)

Hằng đẳng thức: \(\left(a-b\right)^2=a^2-2ab+b^2\).

a.\(\left(x-3\right)^2+2\left(x-3\right)\left(x+2\right)+\left(x+2\right)^2\)

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

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

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

b.\(\left(x+5\right)^2-\left(2x+10\right)\left(x-6\right)+\left(x-6\right)^2\)

\(=\left(x+5\right)^2-2\left(x+5\right)\left(x-6\right)+\left(x-6\right)^2\)

\(=\left[\left(x+5\right)-\left(x-6\right)\right]^2\)

\(=\left(x+5-x+6\right)^2\)

Trả lời:

a, ( x - 3 )² + 2 ( x - 3 ) ( x + 2 ) + ( x + 2 )² 

= ( x - 3 + x + 2 )²

= ( 2x - 1 )²

b, ( x + 5 )² - ( 2x + 10 ) ( x - 6 ) + ( x - 6 )²

= ( x + 5 )² - 2 ( x + 5 ) ( x - 6 ) + ( x - 6 )²

= [ ( x + 5 ) - ( x - 6 ) ]²

= ( x + 5 - x + 6 )²

= 11²

= 121 

\(9\left(x-3y\right)^2-25\left(2x+y\right)^2\)

\(=\left[3\left(x-3y\right)\right]^2-\left[5\left(2x+y\right)\right]^2\)

\(=\left(3x-9y\right)^2-\left(10x+5y\right)^2\)

\(=\left[3x-9y+10x+5y\right]\left[3x-9y-\left(10x+5y\right)\right]\)

\(=\left(13x-4y\right)\left(-7x-14y\right)\)

\(=-7\left(x+2y\right)\left(13x-4y\right)\)

9(x - 3y)² - 25(2x + y)²

= 3².(x - 3y)² - 5².(2x + y)²

= (3x - 9y)² - (10x + 5y)²

= (3x - 9y - 10x - 5y)(3x - 9y + 10x + 5y)

= (-7x - 14y)(13x - 4y)

= -7(x + 2y)(13x - 4y)

(x² + 3²)² 

^{=x^4 + 18x^2+81}

(x² + 3²)² 

= (x²)² + 2x² . 3² + (3²)² 

= x⁴ + 18x² + 81

a) (x + 3)² - 2(x + 3)(x - 2) + (x - 2)² 

= (x + 3 - x + 2)² = 5² = 25

b) (2x + 5)² + 2(2x + 5)(3x - 1) + (3x - 1)² 

= (2x  + 5 + 3x - 1)² = (5x  + 4)²

Trả lời:

a/ ( x + 3 )² - 2 ( x + 3 ) ( x - 2 ) + ( x - 2 )²

=  [ ( x + 3 ) - ( x - 2 ) ]² 

= ( x + 3 - x + 2 )²

= 5²

= 25

b/ ( 2x + 5 )² + 2 ( 2x + 5 ) ( 3x - 1 ) + ( 3x - 1 )²

= ( 2x + 5 + 3x - 1 )²

= ( 5x + 4 )²

\(2.\left(3+1\right).\left(3^2+1\right).\left(3^4+1\right)\)

= \(\left(6+2\right)\left(3^2+1\right)\left(3^4+1\right)\)

= \(\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\)

= \(\left(3^4-1\right)\left(3^4+1\right)\)

= \(3^8-1\)

Chúc bạn học tốt !!!

\(2\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\)

\(=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\)

\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\)

\(=\left(3^4-1\right)\left(3^4+1\right)\)

\(=3^8-1\)

$2.\left(3+1\right).\left({}^{}+1\right).\left({}^{}+1\right)$

= $\left(6+2\right)\left({}^{}+1\right)\left({}^{}+1\right)$

= $\left({}^{}-1\right)\left({}^{}+1\right)\left({}^{}+1\right)$

= $\left({}^{}-1\right)\left({}^{}+1\right)$

= ${}^{}-1$

Chúc bạn học tốt !!

a) Ta có: \(a^3y^3+125\)

\(=\left(ay+5\right)\left(a^2y^2-5ay+25\right)\)

b) Ta có: \(8x^3-y^3-6xy\cdot\left(2x-y\right)\)

\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)-6xy\left(2x-y\right)\)

\(=\left(2x-y\right)\left(4x^2+2xy-6xy+y^2\right)\)

\(=\left(2x-y\right)^3\)