Question

Tính:

a, (a + b) . [(a - b)² + ab]

b, (a - b) . [(a+b)² - ab]

c, (a + b)³ - (a - b)³

d, (a - b)³ + (a + b)³

Answer 1

\(\left(a-b\right)\left[\left(a+b\right)^2-ab\right]\\ =\left(a-b\right)\left(a^2+ab+b^2\right)=a^3-b^3\\ \left(a+b\right)^3-\left(a-b\right)^3\\ =\left(a+b-a+b\right)\left(\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right)\\ =2b\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)\\ =2b\left(3a^2+b^2\right)\\ \left(a-b\right)^3+\left(a+b\right)^3\\ =\left(a-b+a+b\right)\left(\left(a-b\right)^2-\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\right)\\ =2a\left(a^2-2ab+b^2-a^2+b^2+a^2+2ab+b^2\right)\\ =2a\left(a^2+3b^2\right)\)

Answer 2

a, (a + b) . [( a^2 - 2ab + b^2) + ab]

=(a + b) . [a^2 + ( -2ab + ab ) + b^2]

=(a + b) . [a^2 - ab +b^2]

=(a + b)^3

Answer 3

b, Kết quả là (a - b)^3

c, Kết quả là 2b(3a^2 + b^2)

d, Kết quả là 2a(a^2 +3b^2)