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

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

\(=\left[a^2-\left(b^2-2bc+c^2\right)\right].\left[\left(b^2+2bc+c^2\right)-a^2\right]\)

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

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

\(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)

\(=\left[\left(a-b\right)^2-3^2\right].\left[\left(a+b\right)^2-1\right]\)

\(=\left(a-b-3\right)\left(a-b+3\right)\left(a+b-1\right)\left(a+b+1\right)\)

Tham khảo nhé~

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 )

`a^2 + ab + 2a + 2b = a(a+2) + b(a+2) = (a+b)(a+2)`

\(\left(ax+by\right)^2-\left(ay+bx\right)^2\)

\(=\left(ax+by+ay+bx\right)\left(ax+by-ay-bx\right)\)

\(=\left[a\left(x+y\right)+b\left(x+y\right)\right]\left[a\left(x-y\right)-b\left(x-y\right)\right]\)

\(=\left(a+b\right)\left(a-b\right)\left(x+y\right)\left(x-y\right)\)

\(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)

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

\(=\left[a^2+b^2-5+2ab+4\right]\left[a^2+b^2-5-2ab-4\right]\)

\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-9\right]\)

\(=\left(a+b-1\right)\left(a+b+1\right)\left(a-b-3\right)\left(a-b+3\right)\)

a)

(ax+by)² - (ay+bx)²

=(ax+by-ay-bx)(ax+by+ay+bx)

=[ a(x-y) -b(x-y)][ a(x+y) + b(x+y)]

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

b)(a²+b²-5)² - 4(ab+2)²

=(a²+b²-5-2ab-4)(a²+b²-5+2ab+4)

=[ (a-b)² -9][ (a+b)² -1]

=(a-b-3)(a-b+3)(a+b-1)(a+b+1)

a, \(\left(ax+by\right)^2-\left(ay+bx\right)^2\)

\(=\left(ax+ay+bx+by\right)\left(ax-ay+bx-by\right)\)

\(=\left(a+b\right)\left(x+y\right)\left(a-b\right)\left(x-y\right)\)

b, \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)

\(=\left[\left(a-b\right)^2-9\right]\left[\left(a+b\right)^2-1\right]\)

\(=\left(a-b-3\right)\left(a-b+3\right)\left(a+b+1\right)\left(a+b-1\right)\)

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

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

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

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

bố éo biết

\(a\left(b^2+c^2+bc\right)+b\left(c^2+a^2+ac\right)+c\left(a^2+b^2+ab\right)\)

\(=ab^2+ac^2+abc+bc^2+ba^2+abc+ac^2+bc^2+abc\)

\(=c^2\left(b+a\right)+\left(b^2+3\text{a}b+a^2\right)c+ab^2+a^2b\)

\(=bc^2+ac^2+b^2c+3\text{a}bc+a^2c+ab^2+a^2b\)

\(=\left(c+b+a\right)\left(bc+ac+ab\right)\)

a, 4y(x-1)-(1-x)

=(x-1)(4y+1)

b,3x(z+2)+5(-x-2)

=3x(z+2)-5(x+2)

=(z+2)(3x-5)

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

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

\(C=\left(9x^2-1\right)-\left(3x-1\right)^2=\left(3x-1\right)\left(3x+1\right)-\left(3x-1\right)^2=\left(3x-1\right)\left(3x+1-3x+1\right)=2\left(3x+1\right)\)

\(D=x^3-16x=x\left(x^2-16\right)=x\left(x-4\right)\left(x+4\right)\)

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

\(G=\left(2x+3\right)^2-\left(2x-3\right)^2=\left(2x+3-2x+3\right)\left(2x+3+3x-3\right)=6.4x=24x\)

\(A=2x\left(2x+3\right)\\ B=\left(2x+3\right)\left(2x+3-x\right)=\left(2x+3\right)\left(x+3\right)\\ C=\left(3x-1\right)\left(3x+1\right)-\left(3x-1\right)^2\\ =\left(3x-1\right)\left(3x+1-3x+1\right)\\ =2\left(3x-1\right)\\ D=x\left(x^2-16\right)=x\left(x-4\right)\left(x+4\right)\\ E=\left(2x-5y\right)\left(2x+5y\right)\\ G=\left(2x+3-2x+3\right)\left(2x+3+2x-3\right)\\ =24x\)