Trả lời:

Ta có: \(A=\left(x^2+x\right)^2+5y\left(x^2+x\right)+6y^2\)

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

\(=\left[\left(x^2+x\right)^2+2y\left(x^2+x\right)\right]+\left[3y\left(x^2+x\right)+6y^2\right]\)

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

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

ta có :

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

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

\(A=\left(x^2-5x-4\right)^2+7\left(x^2-5x-4\right)+10\)

Đặt \(t=x^2-5x-4\).

\(A=t^2+7t+10=t^2+2t+5t+10=\left(t+2\right)\left(t+5\right)\)

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

\(=\left(x^2-5x-2\right)\left(x^2-5x+1\right)\)

ko k cho mình nha team mình có người k cho mình 3 k nên bạn ko k cho mình 3 câu trả lời 

a.(−4xy)(2xy^2–3x^2y)

=(−4xy)(2xy^2)+(−4xy)(−3x^2y)

=−8x^2y^3+12x^3y^2

nha bạn chúc bạn học tốt ạ 

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

    = \(-8x^2y^3\)\(+12x^3y^2\)

b) = \(\left(-5x\right)\left(3x^3\right)\)\(+\left(-5x\right)\left(7x^2\right)\)\(+\left(5x\right)\left(-x\right)\)

    = \(-15x^4-35x^3+5x^2\)

Với |x| = 2 khi x = 2 hoặc x = -2 

a, \(A=\left(3x+5\right)\left(2x-1\right)+\left(4x-1\right)\left(3x+2\right)\)

\(=6x^2+7x-5+12x^2+5x-2=18x^2+12x-7\)

Với x = 2 thì \(A=89\)

Với x = -2 thì \(A=41\)

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

\(=x^4+x^3y-x^3y-x^2y^2+x^2y^2+xy^3-xy^3-y^4=x^4-y^4\)

Thay x = 2 ; y = -1/4 ta được : \(=16-\frac{1}{256}=\frac{4095}{256}\)

Bài 4 : 

a, \(3\left(1-4x\right)\left(x-1\right)+4\left(3x-2\right)\left(x+3\right)=-27\)

\(\Leftrightarrow3\left(x-1-4x^2+4x\right)+4\left(3x^2+7x-6\right)=-27\)

\(\Leftrightarrow-12x^2+15x-3+12x^2+28x-24=-27\)

\(\Leftrightarrow43x=0\Leftrightarrow x=0\)

b, \(\left(2x+3\right)\left(x-4\right)+\left(x-5\right)\left(x-2\right)=\left(3x-5\right)\left(x-4\right)\)

\(\Leftrightarrow2x^2-5x-12+x^2-7x+10=3x^2-17x+20\)

\(\Leftrightarrow-12x-2=-17x+20\Leftrightarrow5x=22\Leftrightarrow x=\frac{22}{5}\)

( x + 3 )( x + 4 )( x + 5 )( x + 6 ) + 1 

= [ ( x + 3 )( x + 6 ) ][ ( x + 4 )( x + 5 ) ] + 1

= ( x² + 9x + 18 )( x² + 9x + 20 ) + 1

= ( x² + 9x + 19 - 1 )( x² + 9x + 19 + 1 ) 1 

= ( x² + 9x + 19 )² - 1² + 1 = ( x² + 9x + 19 )²

x² - 2x( y + 2 ) + y² + 4y + 4

= x² - 2x( y + 2 ) + ( y + 2 )²

= ( x - y - 2 )²

(-a-b)²=[-1(a+b)]²=(-1)²(a+b)²=(a+b)² (đpcm)

(–a – b)2 = [(– 1).(a + b)]2

 = (–1)2(a + b)2

 = 1.(a + b)2

 = (a + b)2 (đpcm)

thêm x²+y²+z²=1 nha

thêm x² + y² + z² = 1 nha

      HT nha vinh

\(ab+bc+ca\ge3\sqrt[3]{a^2b^2c^2}=3\sqrt[3]{9}\)

Dấu \(=\)khi \(a=b=c=\sqrt[3]{3}\).