(X-y-4)²-(2x+3y-1)²

=(X-Y-4-2X-3Y+1)(X-Y-4+2X+3Y-1)=(-X-4Y-3)(X+2Y-5)

(2x²+1)²+6(2x²+1)+9

=(2X²+1+3)²   (dùng hằng đẳng thức a² +2ab+b² =(a+b)²

=(2x²+4)²=(2(x²+2))²=4(x²+2)²

\(a,\left(x-y-4\right)^2-\left(2x+3y-1\right)^2\)

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

\(b,\left(2x^2+1\right)^2+6\left(2x^2+1\right)+9\)

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

Ta có : \(\left(x-y-4\right)^2\)    \(-\left(2x+3y-1\right)^2\) \(=\left(x-y-4-2x-3y+1\right)\left(x-y-4+2x+3y-1\right)\)

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

Ta có : \(\left(2x^2+1\right)^2+6\left(2x^2+1\right)+9\)\(=\left(2x^2+1\right)^2+2.\left(2x^2+1\right).3+3^2\)

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

\(36x^2-\left(3x-2\right)^2\)

\(=\left(6x\right)^2-\left(3x-2\right)^2\)

\(=\left(6x+3x-2\right)\left(6x-3x+2\right)\)

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

\(-49x^2+9\)

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

\(=\left(3-7x\right)\left(3+7x\right)\)

\(x^6-\frac{1}{64}\)

\(=\left(x^3\right)^2-\left(\frac{1}{8}\right)^2\)

\(=\left(x^3-\frac{1}{8}\right)\left(x^3+\frac{1}{8}\right)\)

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

Ta có: \(2x^4+6x^3+9x^2+6x+1=2x^4+2x^3+4x^3+4x^2+5x^2+5x+x+1\)

\(=\left(2x^4+2x^3\right)+\left(4x^3+4x^2\right)+\left(5x^2+5x\right)+\left(x+1\right)\)

\(=2x^3\left(x+1\right)+4x^2\left(x+1\right)+5x\left(x+1\right)+\left(x+1\right)\)

\(=\left(2x^3+4x^2+5x+1\right)\left(x+1\right)\)

a) 16(4x+5)² - 25(2x+2)²

^{\(=\left[4\left(4x+5\right)\right]^2-\left[5\left(2x+2\right)\right]^2\)}

^{\(=\left[4\left(4x+5\right)+5\left(2x+2\right)\right]\left[4\left(4x+5\right)-5\left(2x+2\right)\right]\)}

^{\(=\left(16x+20+10x+10\right)\left(16x+20-10x-10\right)\)}

^{\(=\left(26x+30\right)\left(6x+10\right)\)}

\(b,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)

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

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

\(c,\left(x+1\right)^4-\left(x-1\right)^4\)

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

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

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

\(=\left(2x^2+2\right)2x.2\)

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

\(=8x\left(x^2+1\right)\)

\(d,16x^2-24xy+9y^2\)

\(=\left(4x\right)^2-2.4.3xy+\left(3y\right)^2\)

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

\(e,a^2-b^2+4bc-4c^2\)

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

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

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

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

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

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

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

1. 2x² - 18 = 2 • (x² - 9) = 2 . (x-3).(x+3)

2.x²- 7xy+ 10y²=((x²) - 7xy) + (2•5y²)=(x - 2y)•(x - 5y)

3.16x³y+0.5y² =((16 • (x³)) • y) + (— • y²) 2= y² ((16 • (x³)) • y) +\(\dfrac{y^2}{2}\)= (2⁴x³ • y) + \(\dfrac{y^2}{2}\)

= \(\dfrac{\text{24x3y • 2 + y2}}{2}\) =\(\dfrac{\text{32x^3y + y2}}{2}\) = 32x³y + y² = y • (32x³ + y) = \(\dfrac{\text{y • (32x^3 + y) }}{2}\)

4.x⁴-4x³+4x² = ((x⁴) - (4 • (x³))) + 2²x² =((x⁴) - 2²x³) + 2²x² = x⁴ - 4x³ + 4x²

= x² • (x² - 4x + 4) = x² • (x - 2)²

^5.2ab²-a²b-b³ = (2ab² - a²b) - b³

= -a²b + 2ab² - b³ = -b • (a² - 2ab + b²)

= -b • (a - b)²

^{Nhớ cho đúng nha}

\(a^2-6a+5=\left(a^2-5a\right)-\left(a-5\right)=a\left(a-5\right)-\left(a-5\right)=\left(a-1\right)\left(a-5\right)\) 

\(a^2-7a+12=\left(a^2-3a\right)-\left(4a-12\right)=a\left(a-3\right)-4\left(a-3\right)=\left(a-4\right)\left(a-3\right)\) 

\(4a^2+4a-3=4a^2-2a+\left(6a-3\right)=2a\left(2a-1\right)+3\left(2a-1\right)=\left(2a+3\right)\left(2a-1\right)\)

X² - 6x + 5

= x² - 6x + 5 + 4 - 4 

= x² - 6x + 9 - 2²

= ( x - 3 )² - 2² 

= ( x - 3 - 2 ) ( x - 3 + 2 ) 

X² - 7x + 12

= X² - 7x + 12 + 0.25 - 0,25

= X² - 7x + 12,25 - ( 0,5 )²

= ( X - 3,5 )² -  ( 0,5 )²

= ( X - 3,5 - 0,5 ) ( X - 3,5 + 0,5 )

4x⁴ - 9x²

= 4x² . x² - 9x² 

= (4x² - 9)x²

Ko chắc đâu bạn ak!

\(4x^4-9x^2\)

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

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

25-a²+4ab-4b² 

= 25-(a² -4ab+4b²)=5²-(a-2b)² =(5-a+2b)(5+a-2b)

7x²-14xy²+7y⁴

=7(x²-2xy+y²)=7(x-y)²

X²+4x-y²+4

= (x²+4x+4)-y²=(x+2)²-y²=(x+2-y)(x+2+y)

4x⁴-9x²

=x²(4x²-9)=x²(2x-3)(2x+3)

2x³-8x²+8x =2x(x²-4x+4)=2x(x-2)²

6xy+5x-5y-3x²-3y²

=(-3x²-3y²+6xy)+5(x-y)=-3(x²-2xy+y²)+5(x-y)=-3(x-y)²+5(x-y)=(x-y)(5+3y-3x)