Question

1. Phân tích các đa thức sau thành nhân tử:

a/x²-y²-5x+5y b/16x²-(x+y)² c/5x²+6xy+y²

d/a²-2a+2b-b²

Answer 1

a) x²-y²-5x+5y=(x²-y²)-(5x-5y)

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

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

b) 16x²-(x+y)²=(4x)²-(x+y)²

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

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

c) 5x²+6xy+y²=5x²+5xy+xy+y²

=5x(x+y)+y(x+y)

=(x+y)(5x+y)

d) a²-2a+2b-b²=( a²-b²)-(2a-2b)

= (a-b)(a+b)-2(a-b)

=(a-b)(a+b-2)

Answer 2

a) x² - y² - 5x + 5y

= (x² - y²) - (5x - 5y)

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

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

b) 16x² - (x + y)²

= (4x)² - (x + y)²

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

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

c) 5x² + 6xy + y²

= 5x² + 5xy + xy + y²

= 5x(x + y) + y(x + y)

= (x + y)(5x + y)

d) a² - 2a + 2b - b²

= (a² - b²) - (2a - 2b)

= (a - b)(a + b) - 2(a - b)

= (a - b)(a + b - 2)

Answer 3

a,x\(^2\)-y\(^2\)-5x+5y

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

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

Answer 4

b,16\(\)x\(^2\)-(x+y)\(^2\)

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

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

Answer 5

c,5x\(^2\)+6xy+y\(^2\)

=5x(x+y)+y(x+y)

=(x+y)(5x+y)

Answer 6

d,a\(^2\)-2a+2b-b\(^2\)

=(a-b)(a+b)-2(a-b)

=(a-b)(a+b-2)