a) \(\left(a^2+b^2-5\right)^2-2\left(ab+2\right)^2\)

\(=\left(a^2+b^2-5\right)^2-\left(\sqrt{2}.ab+\sqrt{2}.2\right)^2\)

\(=\left(a^2+b^2-5-\sqrt{2}.ab-\sqrt{2}.2\right).\left(a^2+b^2-5+\sqrt{2}.ab+\sqrt{2}.2\right)\)

b) \(\left(4a^2-3a-18\right)^2-\left(4a^2+3a\right)^2\)

\(\left(4a^2-3a-18-4a^2-3a\right).\left(4a^2-3a-18+4a^2+3a\right)\)

\(=\left(-6a-18\right).\left(8a^2-18\right)\)

\(=\left(-6\right).\left(a+3\right).2.\left(4a^2-9\right)\)

\(=\left(-12\right).\left(a+3\right).\left(2a-3\right).\left(2a+3\right)\)

a) Xem lại đề

b) ( 4a² - 3a - 18 )² - ( 4a² + 3a )²

= [ ( 4a² - 3a - 18 ) - ( 4a² + 3a ) ][ ( 4a² - 3a - 18 )​ + ( 4a² + 3a ) ]

= ( 4a² - 3a - 18 - 4a² - 3a )( 4a² - 3a - 18 + 4a² + 3a )

= ( -6a - 18 )( 8a² - 18 )

= -6( a + 3 ).2( 4a² - 9 )

= -12( a + 3 )( 4a² - 9 )

= -12( a + 3 )( 2a - 3 )( 2a + 3 )

a. ( a² + b² - 5 )² - 2 ( ab + 2 )²

= ( a² + b² - 5 )² - [\(\sqrt{2}\)( ab + 2 ) ]²

= [ a² + b² - 5 -\(\sqrt{2}\)( ab + 2 ) ] [ a² + b² - 5 +\(\sqrt{2}\)( ab + 2 ) ]

= ( a² + b² - 5 -\(\sqrt{2}\)ab - 2\(\sqrt{2}\)) ( a² + b² - 5 +\(\sqrt{2}\)ab + 2\(\sqrt{2}\) )

b. ( 4a² - 3a - 18 )² - ( 4a² + 3a )²

= ( 4a² - 3a - 18 - 4a² - 3a ) ( 4a² - 3a - 18 + 4a² + 3a )

= ( - 6a - 18 ) ( 8a² - 18 )

= - 6 ( a + 3 ) . 2 [ ( 2a )² - 3² ]

= - 12 ( 2a - 3 ) ( 2a + 3 )

\(\left(x+a\right)\left(x+2a\right)\left(x+3a\right)\left(x+4a\right)+a^4.\)

\(=\left(x+a\right)\left(x+4a\right)\left(x+2a\right)\left(x+3a\right)+a^4.\)

\(=\left(x^2+5ax+4a^2\right)\left(x^2+5ax+6a^2\right)+a^4.\)

\(=\left(x+5ax+4a^2+a^2\right)^2.\)

\(=\left(x+5ax+5a^2\right)^2.\)

\(\left(x+a\right)\left(x+2a\right)\left(x+3a\right)\left(x+4a\right)+a^4\)

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

\(=\)\(\left(x^2+5ax+4a^2\right)\left(x^2+5ax+6a^2\right)+a^4\)

\(=\)\(\left[\left(x^2+5ax+5a^2\right)-a^2\right].\left[\left(x^2+5ax+5a^2\right)-a^2\right]+a^4\)

\(=\)\(\left(x^2+5ax+5a^2\right)^2-a^4+a^4\)

\(=\)\(\left(x^2+5ax+5a^2\right)^2\)

Chúc bạn học tốt ~ 

(x + a)(x + 2a)(x + 3a)(x + 4a) + a⁴

= (x + a)(x + 4a)(x + 2a)(x + 3a) + a⁴

= (x² + 4ax + ax + 4a²)(x² + 3ax + 2ax + 6a²) + a⁴

= (x² + 5ax + 4a²)(x² + 5ax + 6a²) + a⁴

Đặt x² + 5ax + 4a² = t

= t(t + 2a²) + a⁴

= (t + a²)²

= (x² + 5ax + 4a² + a²)²

= (x² + 5ax + 5a²)²

đơn giản

Cách đặt khác ez hơn :))

\(A=\left(x+a\right)\left(x+2a\right)\left(x+3a\right)\left(x+4a\right)+a^4\)

\(A=\left[\left(x+a\right)\left(x+4a\right)\right]\left[\left(x+2a\right)\left(x+3a\right)\right]+a^4\)

\(A=\left(4a^2+5ax+x^2\right)\left(6a^2+5ax+x^2\right)+a^4\)

Đặt \(p=5a^2+5ax+x^2\)

\(\Rightarrow A=\left(p-a^2\right)\left(p+a^2\right)+a^4\)

\(\Rightarrow A=p^2-a^4+a^4\)

\(\Rightarrow A=p^2\)

Thay \(p=5a^2+5ax+x^2\)vào A ta có :

\(A=\left(5a^2+5ax+x^2\right)^2\)

\(4a^2b^2-\left(a^2+b^2-1\right)^2\)

\(=\left[2ab-\left(a^2+b^2-1\right)\right].\left[2ab+\left(a^2+b^2-1\right)\right]\)

\(=\left(2ab-a^2-b^2+1\right)\left(2ab+a^2+b^2+-1\right)\)

\(=\left[1-\left(a-b\right)^2\right]\left[\left(a+b\right)^2-1\right]\)

\(=\left(1-a+b\right)\left(1+a-b\right)\left(a+b+1\right)\left(a+b-1\right)\)

\(4a^2b^2-\left(a^2+b^2-1\right)^2=\left(2ab+a^2+b^2-1\right)\left(2ab-a^2-b^2+1\right)\)

\(=\left[\left(a+b\right)^2-1\right]\left[1-\left(a-b\right)^2\right]\)

\(=\left(a+b-1\right)\left(a+b+1\right)\left(1+a-b\right)\left(1-a+b\right)\)

`a, 4a^2 + 4a + 1 = (2a+1)^2`

`b, -3x^2 + 6xy - 3y^2`

` = -3(x-y)^2`

`c, (x+y)^2 - 2(x+y)z + z^2`

`= (x+y-z)^2`

=\(\left(x+a-3\right)\left(x^2-2ax-2x+4a-12\right)\)

4a²b²-(a²+b²-c²)²

= (4ab-a²-b²+c²)(4ab+a²+b²-c²)

= -[(a-b)²-c²][(a+b)²-c²]

=-(a-b+c)(a-b-c)(a+b-c)(a+b+c)

=(b-a-c)(b+c-a)(a+b-c)(a+b+c)

\(4a^2b^2-\left(a^2+b^2-c^2\right)^2\)

\(=\left(2ab\right)^2-\left(a^2+b^2-c^2\right)^2\)

\(=\left(2ab-a^2-b^2+c^2\right)\left(2ab+a^2+b^2-c^2\right)\)

a) x(y - x)³ + y(x - y)² + xy(x - y)

= x(y - x).(y - x)² +  y(x - y)² + xy(x - y)

= x(y - x)(x - y)² + y(x - y)² + xy(x - y)

= (x - y)[x(y - x)(x - y) + y(x - y) + xy]

= (x - y)[x(y - x)(x - y) + y(x - y) + xy]

b) 3a²x - 3a²y + abx - aby

= 3a²(x - y) + ab(x - y)

= a(x - y)(3a + b)

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

= -x( x - y )³ - y( x - y )² + xy( x - y )

= ( x - y )[ -x( x - y )² - y( x - y ) + xy ]

= ( x - y )[ -x( x² - 2xy + y² ) - yx + y² + xy ]

= ( x - y )( -x³ + 2x²y - xy² - yx + y² + xy )

= ( x - y )( -x³ + 2x²y - xy² + y² )

b) 3a²x - 3a²y + abx - aby

= 3a²( x - y ) + ab( x - y )

= ( x - y )( 3a² + ab )

= ( x - y )a( 3a + b )

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

= -x (x - y) 3  - y (x - y) 2  + xy (x - y)

= (x - y) [-x (x - y) 2  - y (x - y) + xy]

= (x - y) [-x (x 2  - 2xy + y 2  ) - yx + y 2  + xy]

= (x - y) (-x 3  + 2x 2 y - xy 2  - yx + y 2  + xy)

= (x - y) (-x 3  + 2x 2 y - xy 2  + y 2  )

b) 3a 2 x - 3a 2 y + abx - aby

= 3a 2 (x - y) + ab (x - y)

= (x - y) (3a 2  + ab)

= (x - y) a (3a + b)học tốt

Ta có:

(x+a)(x+2a)(x+3a)(x+4a) + a⁴

=(x+a)(x+4a)(x+3a)(x+2a) +a⁴

=(x²+5ax+4a²)(x²+5ax+6a²) + a⁴

Đặt x²+5ax+5a²=y

=>(x²+5ax+4a²)(x²+5ax+6a²) + a⁴=(y-a²)(y+a²)+a⁴

=y²-a⁴+a⁴

=y²

=(x²+5ax+5a²)²

k mik nha