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\(\left(1-x^2\right)-4x\left(1-x^2\right)\)
\(=\left(1-x^2\right)\left(1-x^2-4x\right)\)
\(=\left(1-x^2\right)\left(1-x\right)^2\)
\(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(=\left(ax+by+ay+bx\right)\left(ax+by-ay-bx\right)\)
\(=\left[a\left(x+y\right)+b\left(x+y\right)\right]\left[a\left(x-y\right)-b\left(x-y\right)\right]\)
\(=\left(a+b\right)\left(a-b\right)\left(x+y\right)\left(x-y\right)\)
\(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left[\left(a^2+b^2-5\right)+2\left(ab+2\right)\right]\left[\left(a^2+b^2-5\right)-2\left(ab+2\right)\right]\)
\(=\left[a^2+b^2-5+2ab+4\right]\left[a^2+b^2-5-2ab-4\right]\)
\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-9\right]\)
\(=\left(a+b-1\right)\left(a+b+1\right)\left(a-b-3\right)\left(a-b+3\right)\)
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)
\(\left(ab+1\right)^2-\left(a+b\right)^2=\left(ab+1+a+b\right)\left(ab+1-a-b\right).\)
\(=\left(a+1\right)\left(b+1\right)\left(a-1\right)\left(b-1\right)\)
\\(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\)
\(=\left(x+1+2y+1\right)\left(x+1-2y-1\right)=\left(x+2y+2\right)\left(x-2y\right)\)
\(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\)
\(=\left[a^2-\left(b^2-2bc+c^2\right)\right].\left[\left(b^2+2bc+c^2\right)-a^2\right]\)
\(=\left[a^2-\left(b-c\right)^2\right].\left[\left(b+c\right)^2-a^2\right]\)
\(=\left(a-b+c\right)\left(a+b-c\right)\left(b+c-a\right)\left(b+c+a\right)\)
\(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)
\(=\left[\left(a-b\right)^2-3^2\right].\left[\left(a+b\right)^2-1\right]\)
\(=\left(a-b-3\right)\left(a-b+3\right)\left(a+b-1\right)\left(a+b+1\right)\)
Tham khảo nhé~
\(a\left(b^2+c^2+bc\right)+b\left(c^2+a^2+ac\right)+c\left(a^2+b^2+ab\right)\)
\(=ab^2+ac^2+abc+bc^2+ba^2+abc+ac^2+bc^2+abc\)
\(=c^2\left(b+a\right)+\left(b^2+3\text{a}b+a^2\right)c+ab^2+a^2b\)
\(=bc^2+ac^2+b^2c+3\text{a}bc+a^2c+ab^2+a^2b\)
\(=\left(c+b+a\right)\left(bc+ac+ab\right)\)
a) \(\left(a^2+b^2-5\right)^2-2\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left(\sqrt{2}.ab+\sqrt{2}.2\right)^2\)
\(=\left(a^2+b^2-5-\sqrt{2}.ab-\sqrt{2}.2\right).\left(a^2+b^2-5+\sqrt{2}.ab+\sqrt{2}.2\right)\)
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 )
(ab-1)2 + (a+b)2
= a2b2 - 2ab + 1 + a2 + 2ab + b2
= a2b2 + 1 + a2 + b2
= a2.(b2+1) + (1+b2)
= (a2+1).(b2+1)