1. (x + y)² - 6(x + y) + 9 = (x + y)² - 2(x + y).3 + 3² = (x + y - 3)²

2. 4 - 36x + 81x² = 2² - 2.4.9x + (9x)² = (2 - 9x)²

3. 9x² - 24xy + 15y² = (3x)² - 2.3x.4y + (4y)² - y² = (3x - 4y)² - y²

= (3x - 4y - y)(3x - 4y + y) = (3x - 5y)(3x - 3y) = 3(x - y)(3x - 5y)

4. a² - 25b² + 50bc - 25c² = a² - [(5b)² - 2.5b.5c + (5c)²]

= a² - (5b - 5c)² = (a - 5b + 5c)(a + 5b - 5c)

 a) 3x2 – 7x + 2

\(=3x^2-6x-x+2\)

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

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

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

 b) a(x2 + 1) – x(a2 + 1)

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

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

.......?

a) Ta có: \(3x^2-7x+2\)

\(=3x^2-6x-x+2\)

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

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

b) Ta có: \(a\left(x^2+1\right)-x\left(a^2+1\right)\)

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

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

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

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

c) Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)

\(=\left(x^2+7x\right)^2+16\left(x^2+7x\right)+6\left(x^2+7x\right)+96\)

\(=\left(x^2+7x\right)\left(x^2+7x+16\right)+6\left(x^2+7x+16\right)\)

\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)\)

\(=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)

d) Ta có: \(\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)

\(=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)

\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+105+15\)

\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+120\)

\(=\left(a^2+8a\right)^2+12\left(a^2+8a\right)+10\left(a^2+8a\right)+120\)

\(=\left(a^2+8a\right)\left(a^2+8a+12\right)+10\left(a^2+8a+12\right)\)

\(=\left(a^2+8a+12\right)\left(a^2+8a+10\right)\)

\(=\left(a+2\right)\left(a+6\right)\left(a^2+8a+10\right)\)

1a) 5x - 5y + 3x (x - y)

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

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

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

b) x² + 2xy + y² - 4

= (x² + 2xy + y²) - 2²

= (x + y)² - 2²

= [(x + y) + 2] [(x + y) - 2]

= (x + y + 2) (x + y - 2)

#Học tốt!!!

~NTTH~
 

nó dễ ợt mà -_- 

x²y²+4xy+4=(xy+2)² xong :)) 

\(a,5\left(x-y\right)-3x\left(y-x\right)=5\left(x-y\right)+3x\left(x-y\right)=\left(5+3x\right)\left(x-y\right)\\ b,x^2-4xy+4y^2=\left(x-2y\right)^2\\ c,\left(x+1\right)^2+x\left(5-x\right)=0\\ \Rightarrow x^2+2x+1+5x-x^2=0\\ \Rightarrow7x+1=0\\ \Rightarrow7x=-1\\ \Rightarrow x=-\dfrac{1}{7}\)

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

c: \(\Leftrightarrow x^2-2x+1+5x-x^2=0\)

hay x=-1/3