a) Thể tích của hình hộp chữ nhật đã cho là:

\(x=x\left(\right.x-1\left.\right)\left(\right.x+1\left.\right)=x^3-x\)

b) Tại \(x=4\), thể tích của hình hộp chữ nhật là:

\(x=4^3-4=60\) (đơn vị thể tích)

Vậy ta có phép chia hết và thương là \(� = 2 �^{2} - 3 � + 1\).

a) \(x\left(\right.x\left.\right)+x\left(\right.x\left.\right)\) 

\(=\left(x\right.^4-5x^3+4x-5\left.\right)+\left(\right.-x^4+3x^2+2x+1\left.\right)\)

\(= �^{4} - 5 �^{3} + 4 � - 5 - �^{4} + 3 �^{2} + 2 � + 1\)

\(= \left(\right. �^{4} - �^{4} \left.\right) - 5 �^{3} + 3 �^{2} + \left(\right. 4 � + 2 � \left.\right) + \left(\right. 1 - 5 \left.\right)\)

\(= - 5 �^{3} + 3 �^{2} + 6 � - 4\)

b) \(� \left(\right. � \left.\right) = � \left(\right. � \left.\right) - � \left(\right. � \left.\right)\)

\(= \left(\right. �^{4} - 5 �^{3} + 4 � - 5 \left.\right) - \left(\right. - �^{4} + 3 �^{2} + 2 � + 1 \left.\right)\)

\(= �^{4} - 5 �^{3} + 4 � - 5 + �^{4} - 3 �^{2} - 2 � - 1\)

\(= \left(\right. �^{4} + �^{4} \left.\right) - 5 �^{3} - 3 �^{2} + \left(\right. 4 � - 2 � \left.\right) + \left(\right. - 1 - 5 \left.\right)\)

\(= 2 �^{4} - 5 �^{3} - 3 �^{2} + 2 � - 6\)

a) \(x\left(\right.x\left.\right)+x\left(\right.x\left.\right)\) 

\(=\left(x\right.^4-5x^3+4x-5\left.\right)+\left(\right.-x^4+3x^2+2x+1\left.\right)\)

\(= �^{4} - 5 �^{3} + 4 � - 5 - �^{4} + 3 �^{2} + 2 � + 1\)

\(= \left(\right. �^{4} - �^{4} \left.\right) - 5 �^{3} + 3 �^{2} + \left(\right. 4 � + 2 � \left.\right) + \left(\right. 1 - 5 \left.\right)\)

\(= - 5 �^{3} + 3 �^{2} + 6 � - 4\)

b) \(� \left(\right. � \left.\right) = � \left(\right. � \left.\right) - � \left(\right. � \left.\right)\)

\(= \left(\right. �^{4} - 5 �^{3} + 4 � - 5 \left.\right) - \left(\right. - �^{4} + 3 �^{2} + 2 � + 1 \left.\right)\)

\(= �^{4} - 5 �^{3} + 4 � - 5 + �^{4} - 3 �^{2} - 2 � - 1\)

\(= \left(\right. �^{4} + �^{4} \left.\right) - 5 �^{3} - 3 �^{2} + \left(\right. 4 � - 2 � \left.\right) + \left(\right. - 1 - 5 \left.\right)\)

\(= 2 �^{4} - 5 �^{3} - 3 �^{2} + 2 � - 6\)