Question

Phân tích đa thức thành nhân tử:

a) 49 - a² + 2ab - b²

b) a² - b² + 4bc - 4c²

c) 4b²c² - (b² + c² - a²)²

d) (a + b + c)² + (a + b - c)² -4c²

Answer 1

a)49-a²+2ab-b²=49-(a²-2ab+b²)=49-(a-b)²=(7-a+b)(7+a-b)

b)a²-b²+4bc-4c²=a²-(b²-2bc+c²)=a²-(b-2c)²=(a-b+2c)(a+b-2c)

c)4b²c²-(b²+c²-a²)²=(4bc-b²-c²+a²)(4bc+b²+c²-a²)

d)(a+b+c)²+(a+b-c)²-4c²

=(a+b+c)²+(a+b-c-2c)(a+b-c+2c)

=(a+b+c)²+(a+b-3c)(a+b+c)

=(a+b+c)(a+b+c+a+b-3c)

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

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

Answer 2

a, 49 -a^2 + 2ab - b^2 = 7^2 - ( a^2 - 2ab + b^2) = 7^2 - (a-b)^2 = ( 7-a+b) ( 7 +a -b)

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

c, 4.b^2.c^2 - ( b^2 + c^2 - a^2)^2 = ( 2bc)^2 - ( b^2  + c^2 - a^2)^2 = ( 2bc - b^2 - c^2 +a^2 )( 2bc + b^2 + c^2 - a^2) 

= ( 2bc - b^2 - c^2 +a^2 ) [ (b + c)^2 - a^2) = ( 2bc - b^2 - c^2 +a^2 ) ( b + c -a)(b + c + a)

d, ( a+b+c)^2  +( a + b - c)^2 - 4c^2 = ( a + b + c)^2 + ( a + b - c - 2c)( a + b - c + 2c) = ( a+b +c)^2 + ( a+b - 3c)(a+b+c)

= ( a+b+c)( a+ b+ c + a + b - 3c) = ( a+b+c )( 2a + 2b - 2c) = 2(a+b+c)(a+b-c)