Question

Ứng dụng các hằng đẳng thức đáng nhớ để thực hiện phép tính:

a)\(\left(m+n\right)\left(m^2-mn+n^2\right)\)

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

c)\(\left(1+x+x^2\right)\left(1-x\right)\left(1+x\right)\left(1-x+x^2\right)\)

 

 

Answer 1

a/ \(\left(m+n\right)\left(m^3-mn+n^2\right)=m^3+n^3\)

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

\(\left(1+x+x^2\right)\left(1-x\right)\left(1+x\right)\left(1-x+x^2\right)=\left(\left(1+x+x^2\right)\left(1-x\right)\right)\left(\left(1-x+x^2\right)\left(1+x\right)\right)=\left(1-x^3\right)\left(1+x^3\right)=1-x^6\)

Answer 2

a) m³+n³

b)  (a -b-c+a-b+c)(a-b-c-a+b-c)

= -4c(a-b)

c) (1-x³)(1+x³)

=1-x⁶