a) 5ay - 3bx + ax - 15by

= (5ay + ax) - (3bx + 15by)

= a (5y + x) - 3b (x + 5y)

= (5y + x) (a - 3b)

b) x^3 + x^2 - x - 1

= (x^3 + x^2) - (x + 1)

= x^2 (x + 1) - (x + 1)

= (x + 1) (x^2 - 1)

c) (2a + b)^2 - (2b + a)^2

= 4a^2 + 4ab + b^2 - 4b^2 - 4ab - a^2

= 3a^2 - 3b^2

= 3 (a^2 - b^2)

d) (8a^3 - 27b^3) - 2a (4a^2 - 9b^2)

= 8a^3 - 27b^3 - 8a^3 + 18ab^2

= 27b^3 + 18ab^2

= 9b^2 (3b + 2a)

a, \(\left(8a^3-27b^3\right)-2a\left(4a^2-9b^2\right)\)

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

\(=\left(2a-3b\right)\left[4a^2+6ab+9b^2-2a\left(2a+3b\right)\right]\)

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

\(=\left(2a-3b\right).9b^2\)

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

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

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

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

c, \(\left(m^3+n^3\right)+\left(m+n\right)^2\)

\(=\left(m+n\right)\left(m^2-mn+n^2\right)+\left(m+n\right)^2\)

\(=\left(m+n\right)\left(m^2-mn+n^2+m+n\right)\)

Chúc bạn học tốt!!!

a: \(P=-3x^3+5x\)

\(=x\cdot\left(-3x^2\right)+x\cdot5\)

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

b: \(Q=\left(2x-1\right)+\left(x-2\right)\left(2x-1\right)\)

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

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

c: \(R=4-16x^2\)

\(=4\cdot1-4\cdot4x^2\)

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

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

d: \(S=36-4x^2\)

\(=4\cdot9-4\cdot x^2\)

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

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

e: \(T=8x^3-1\)

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

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

f: \(Q=8-x^3\)

\(=2^3-x^3\)

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

g: \(N=64-x^3\)

\(=4^3-x^3\)

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

`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`

Làm tính nhân

(4x³+3xy²-2y³).(3x²-5xy-6y²)

=12x⁵+12y⁵-20x⁴y-36x²y³-8xy⁴

Phân tích đa thức thành nhân tử

10x³+5x²y-10x²y-10xy²+5y³

=10x³-5x²y-10xy²+5y³

=5(2x³-x²y-2xy²+y³-)

\(a.\) \(ax^2-a^2x-x+a\)

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

\(=ax\left(x-a\right)-\left(x-a\right)\)

\(=\left(ax-1\right)\left(x-a\right)\)

\(b.\) \(18x^3-12x^2+2x\)

\(=2x\left(9x^2-6x+1\right)\)

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

\(c.\) \(x^3-5x^2-4x+20\)

\(=\left(x^3-5x^2\right)-\left(4x-20\right)\)

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

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

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

\(d.\) \(\left(x+7\right)\left(x+15\right)+15\)

\(=x^2+15x+7x+105+15\)

\(=x^2+22x+120\)

\(=\left(x+10\right)\left(x+12\right)\)

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

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

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

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

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

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

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

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 )

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