a2 – b2 – 4a + 4

= a2 – 4a + 4 – b2

= (a – 2)2 – b2

= (a – 2 + b)(a – 2 – b)

= (a + b – 2)(a – b – 2)

a) \(a^2+ab-7a-7b=a\left(a+b\right)-7\left(a+b\right)=\left(a+b\right)\left(a-7\right)\)

b) \(5ab+4c+20b+ac=5b\left(a+4\right)+c\left(a+4\right)=\left(a+4\right)\left(5b+c\right)\)

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

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

\(x^5+x^4+1\)

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

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

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

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

cảm ơn bạn nhiều, không biết còn cách không? Mong nhận đượ giúp đỡ!

ta có :

giups mình với nha

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

\(a^2-b^2-2x\left(a-b\right)\)

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

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

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

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

Lời giải:

$x^2-y^2+a^2-b^2+2ax+2by=(x^2+a^2+2ax)-(y^2+b^2-2by)$

$=(x+a)^2-(y-b)^2=(x+a-y+b)(x+a+y-b)$

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

b) \(=3y\left(4-x^2\right)+9\left(4-x^2\right)=3\left(4-x^2\right)\left(y+3\right)\)

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

a, a² + 4ac + 4c² - 16 = (a + 2c)² - 4² = (a + 2c -4).(a + 2c +4)

b, 12y - 9x² + 36 - 3x²y = (12y + 36) - (3x²y + 9x²) = 12.(y+ 3) - 3x².(y + 3) =(y + 3).(12 - 3x²)