Find the Product:
\[ (1 + x)(1 – x + x^2) \]
Solution:
Using identity:
\[ (a+b)(a^2-ab+b^2)=a^3+b^3 \]
Here, \[ a=1,\qquad b=x \]
\[ (1 + x)(1 – x + x^2) \]
\[ = (1 + x)(1^2 – 1\cdot x + x^2) \]
\[ = 1^3 + x^3 \]
\[ = 1 + x^3 \]
\[ (1 + x)(1 – x + x^2) \]
Using identity:
\[ (a+b)(a^2-ab+b^2)=a^3+b^3 \]
Here, \[ a=1,\qquad b=x \]
\[ (1 + x)(1 – x + x^2) \]
\[ = (1 + x)(1^2 – 1\cdot x + x^2) \]
\[ = 1^3 + x^3 \]
\[ = 1 + x^3 \]