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主要内容

多项式恒等式

问题

小王被问道下列等式是不是恒等式:
left parenthesis, x, squared, plus, 1, right parenthesis, squared, equals, left parenthesis, x, squared, minus, 1, right parenthesis, squared, plus, left parenthesis, 2, x, right parenthesis, squared
他进行了以下运算:
=(x2+1)2步骤 1=x4+x2+x2+1步骤 2=x4+2x2+1步骤 3=x4+2x2+12x2+2x2步骤 4=(x42x2+1)+4x2步骤 5=(x21)2+(2x)2\begin{aligned} &\phantom{=}(x^2+1)^2 \\\\ \xhookrightarrow{\text{步骤 }1}\quad&=x^4+x^2+x^2+1 \\\\ \xhookrightarrow{\text{步骤 }2}\quad&=x^4+2x^2+1 \\\\ \xhookrightarrow{\text{步骤 }3}\quad&=x^4+2x^2+1-2x^2+2x^2 \\\\ \xhookrightarrow{\text{步骤 }4}\quad&=(x^4-2x^2+1)+4x^2 \\\\ \xhookrightarrow{\text{步骤 }5}\quad&=(x^2-1)^2+(2x)^2 \end{aligned}
由于这个原因, 他认为这是恒等式
他正确吗? 如果不正确, 哪步出错了?
选出正确答案:
不会做了?
不会做了?