f(x)=(x-5)^3(x+4)^2 eching

$$f ( x ) = ( x - 5 ) ^ { 3 } ( x + 4 ) ^ { 2 }$$

Baholash

$$\left(x+4\right)^{2}\left(x-5\right)^{3}$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(x-5\right)^{3} kengaytirilishi uchun ishlating.

$$\left(x^{3}-15x^{2}+75x-125\right)\left(x+4\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+4\right)^{2} kengaytirilishi uchun ishlating.

$$\left(x^{3}-15x^{2}+75x-125\right)\left(x^{2}+8x+16\right)$$

x^{3}-15x^{2}+75x-125 ga x^{2}+8x+16 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{5}-7x^{4}-29x^{3}+235x^{2}+200x-2000$$

Kengaytirish

$$x^{5}-7x^{4}-29x^{3}+235x^{2}+200x-2000$$

Yechim qadamlari

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(x-5\right)^{3} kengaytirilishi uchun ishlating.

$$\left(x^{3}-15x^{2}+75x-125\right)\left(x+4\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+4\right)^{2} kengaytirilishi uchun ishlating.

$$\left(x^{3}-15x^{2}+75x-125\right)\left(x^{2}+8x+16\right)$$

x^{3}-15x^{2}+75x-125 ga x^{2}+8x+16 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{5}-7x^{4}-29x^{3}+235x^{2}+200x-2000$$