Question

Rut gọn các biểu thức sau

a) (x+y)^2 - (x-y)^2

b) (a+b)^3 + (a-b)^3 - 2a^3

c) 9^8. 2^8 - (18^4 - 1) (18^4+1)

Answer 1

a, \(\left(x+y\right)^2-\left(x-y\right)^2\)

\(=x^2+2xy+y^2-\left(x^2-2xy+y^2\right)\)

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

\(=4xy\)

b, \(\left(a+b\right)^3+\left(a-b\right)^3-2a^3\)

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

\(=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3-2a^3\)

\(=6ab^2\)

c, \(9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)\)

\(=\left(9.2\right)^8-\left[\left(18^4\right)^2-1^2\right]\)

\(=18^8-\left(18^8-1\right)\)

\(=18^8-18^8+1\)

\(=1\)

Answer 2

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