Question

Phân tích các đẳng thức sau thành nhân tử:

a) a² + 2ab + b² - c² + 2cd - d²

b) xz - yz - x² + 2xy - y²

c) z² - (x - 1)² + 2. (x - 1) - 1

d) a²x + aby - 2abx - 2b²y

e) xy. (m² + n²) - mn. (x² + y²)

g) (ay - bx)² + (xy - ab²)

Answer 1

a) a² + 2ab + b² - c2 + 2cd - d2

= ( a2 + 2ab + b2 ) - ( c2 - 2cd + d\(^2\) )

= ( a + b )\(^2\) - ( c - d )\(^2\)

= ( a + b + c - d ) ( a + b - c + d )

b) xz - yz - x² + 2xy - y\(^2\)

= ( xz - yz ) - ( x\(^2\) - 2xy + y\(^2\) )

= z( x - y ) - ( x - y )\(^2\)

= ( x - y ) ( z - x - y )

d) a2x + aby - 2abx - 2b2y

= ( a\(^2\)x - 2abx ) + ( aby - 2b\(^2\)y )

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

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