(x-1)^3+x^2+2x-3-এর সমাধান করুন

$$( x - 1 ) ^ { 3 } + x ^ { 2 } + 2 x - 3$$

Evaluate

$$\left(x-1\right)\left(x^{2}-x+4\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

$$x^{3}-3x^{2}+3x-1+x^{2}+2x-3$$

Combine -3x^{2} and x^{2} to get -2x^{2}.

$$x^{3}-2x^{2}+3x-1+2x-3$$

Combine 3x and 2x to get 5x.

$$x^{3}-2x^{2}+5x-1-3$$

Subtract 3 from -1 to get -4.

$$x^{3}-2x^{2}+5x-4$$

Expand

$$x^{3}-2x^{2}+5x-4$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

$$x^{3}-3x^{2}+3x-1+x^{2}+2x-3$$

Combine -3x^{2} and x^{2} to get -2x^{2}.

$$x^{3}-2x^{2}+3x-1+2x-3$$

Combine 3x and 2x to get 5x.

$$x^{3}-2x^{2}+5x-1-3$$

Subtract 3 from -1 to get -4.

$$x^{3}-2x^{2}+5x-4$$