Question

(x+1)(x square-x+1)
with solution​

Answer 1

Solution:-

$\qquad\quad {:}\longmapsto\sf (x+1)(x^2-x+1)$

Let's use distributive formula :

${\boxed{\sf (a+b)(c+d)=a (c+d)+b (c+d)}}$

Substitute the values :

$\qquad\quad {:}\longmapsto\sf x (x^2-x+1)+1 (x^2-x+1)$

Simplify :

$\qquad\quad {:}\longmapsto\sf x^3-x^2+x+x^2-x+1$

Now together like variables :

$\qquad\quad {:}\longmapsto\sf x^3-x^2+x^2+x-x+1$

Simplify :

$\qquad\quad {:}\longmapsto\sf x^3+0+0+1$

$\qquad\quad {:}\longmapsto{\underline {\boxed{\bf x^3+1}}}$

Answer 2

Answer:

$Solution:-</p><p></p><p>\qquad\quad {:}\longmapsto\sf (x+1)(x^2-x+1):⟼(x+1)(x </p><p>2</p><p> −x+1)</p><p></p><p>Let's use distributive formula :</p><p></p><p>{\boxed{\sf (a+b)(c+d)=a (c+d)+b (c+d)}} </p><p>(a+b)(c+d)=a(c+d)+b(c+d)</p><p> </p><p> </p><p></p><p>Substitute the values :</p><p></p><p>\qquad\quad {:}\longmapsto\sf x (x^2-x+1)+1 (x^2-x+1):⟼x(x </p><p>2</p><p> −x+1)+1(x </p><p>2</p><p> −x+1)</p><p></p><p>Simplify :</p><p></p><p>\qquad\quad {:}\longmapsto\sf x^3-x^2+x+x^2-x+1:⟼x </p><p>3</p><p> −x </p><p>2</p><p> +x+x </p><p>2</p><p> −x+1</p><p></p><p>Now together like variables :</p><p></p><p>\qquad\quad {:}\longmapsto\sf x^3-x^2+x^2+x-x+1:⟼x </p><p>3</p><p> −x </p><p>2</p><p> +x </p><p>2</p><p> +x−x+1</p><p></p><p>Simplify :</p><p></p><p>\qquad\quad {:}\longmapsto\sf x^3+0+0+1:⟼x </p><p>3</p><p> +0+0+1</p><p></p><p>\qquad\quad {:}\longmapsto{\underline {\boxed{\bf x^3+1}}}:⟼ </p><p>x </p><p>3</p><p> +1</p><p> </p><p> </p><p>$