Issolvi f(x)=(x+4)^2(x-3)^2(x-1)

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

Evalwa

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

Passi tas-Soluzzjonijiet

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

$$\left(x^{2}+8x+16\right)\left(x-3\right)^{2}\left(x-1\right)$$

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

$$\left(x^{2}+8x+16\right)\left(x^{2}-6x+9\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}+8x+16 b'x^{2}-6x+9 u kkombina termini simili.

$$\left(x^{4}+2x^{3}-23x^{2}-24x+144\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{4}+2x^{3}-23x^{2}-24x+144 b'x-1 u kkombina termini simili.

$$x^{5}+x^{4}-25x^{3}-x^{2}+168x-144$$

Espandi

$$x^{5}+x^{4}-25x^{3}-x^{2}+168x-144$$

Passi tas-Soluzzjonijiet

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

$$\left(x^{2}+8x+16\right)\left(x-3\right)^{2}\left(x-1\right)$$

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

$$\left(x^{2}+8x+16\right)\left(x^{2}-6x+9\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}+8x+16 b'x^{2}-6x+9 u kkombina termini simili.

$$\left(x^{4}+2x^{3}-23x^{2}-24x+144\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{4}+2x^{3}-23x^{2}-24x+144 b'x-1 u kkombina termini simili.

$$x^{5}+x^{4}-25x^{3}-x^{2}+168x-144$$