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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} biex tespandi \left(x-5\right)^{3}.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+4\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika x^{3}-15x^{2}+75x-125 b'x^{2}+8x+16 u kkombina termini simili.

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

Espandi

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} biex tespandi \left(x-5\right)^{3}.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+4\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika x^{3}-15x^{2}+75x-125 b'x^{2}+8x+16 u kkombina termini simili.

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