f(x)=3x^2(x-4)(x-2)(x+1)-এর সমাধান করুন

$$f ( x ) = 3 x ^ { 2 } ( x - 4 ) ( x - 2 ) ( x + 1 )$$

Evaluate

$$3\left(x-4\right)\left(x-2\right)\left(x+1\right)x^{2}$$

Solution Steps

Use the distributive property to multiply 3x^{2} by x-4.

$$\left(3x^{3}-12x^{2}\right)\left(x-2\right)\left(x+1\right)$$

Use the distributive property to multiply 3x^{3}-12x^{2} by x-2 and combine like terms.

$$\left(3x^{4}-18x^{3}+24x^{2}\right)\left(x+1\right)$$

Use the distributive property to multiply 3x^{4}-18x^{3}+24x^{2} by x+1 and combine like terms.

$$3x^{5}-15x^{4}+6x^{3}+24x^{2}$$

Expand

$$3x^{5}-15x^{4}+6x^{3}+24x^{2}$$

Solution Steps

Use the distributive property to multiply 3x^{2} by x-4.

$$\left(3x^{3}-12x^{2}\right)\left(x-2\right)\left(x+1\right)$$

Use the distributive property to multiply 3x^{3}-12x^{2} by x-2 and combine like terms.

$$\left(3x^{4}-18x^{3}+24x^{2}\right)\left(x+1\right)$$

Use the distributive property to multiply 3x^{4}-18x^{3}+24x^{2} by x+1 and combine like terms.

$$3x^{5}-15x^{4}+6x^{3}+24x^{2}$$