Question

triển khai biểu thức sau theo hằng đẳng thức:

21) (x-1)(1+x)(1+x²)

22) (x-2)(x+2)(x²+4)

Answer 1

\(21,\left(x-1\right).\left(x+1\right).\left(1+x^2\right)\)
\(=\left(x^2-1^2\right).\left(x^2+1\right)\)
\(=\left(x^2-1\right).\left(x^2+1\right)\)
\(=\left(x^2\right)^2-1^2\)
\(=x^4-1\)
\(22,\left(x-2\right).\left(x+2\right).\left(x^2+4\right)\)
\(=\left(x^2-2^2\right).\left(x^2+4\right)\)
\(=\left(x^2-4\right).\left(x^2+4\right)\)
\(=\left(x^2\right)^2-4^2\)
\(=x^4-16\)

Answer 2

21: \(\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\)

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

\(=\left(x^2\right)^2-1^2=x^4-1\)

22: \(\left(x-2\right)\left(x+2\right)\left(x^2+4\right)\)

\(=\left(x^2-4\right)\left(x^2+4\right)\)

\(=\left(x^2\right)^2-4^2=x^4-16\)