Issolvi 6x(3x-1)^2+2x^2(1-3x)^2

$$6 x ( 3 x - 1 ) ^ { 2 } + 2 x ^ { 2 } ( 1 - 3 x ) ^ { 2 }$$

Evalwa

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(3x-1\right)^{2}.

$$6x\left(9x^{2}-6x+1\right)+2x^{2}\left(1-3x\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 6x b'9x^{2}-6x+1.

$$54x^{3}-36x^{2}+6x+2x^{2}\left(1-3x\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(1-3x\right)^{2}.

$$54x^{3}-36x^{2}+6x+2x^{2}\left(1-6x+9x^{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x^{2} b'1-6x+9x^{2}.

$$54x^{3}-36x^{2}+6x+2x^{2}-12x^{3}+18x^{4}$$

Ikkombina -36x^{2} u 2x^{2} biex tikseb -34x^{2}.

$$54x^{3}-34x^{2}+6x-12x^{3}+18x^{4}$$

Ikkombina 54x^{3} u -12x^{3} biex tikseb 42x^{3}.

$$42x^{3}-34x^{2}+6x+18x^{4}$$

Espandi

$$18x^{4}+42x^{3}-34x^{2}+6x$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(3x-1\right)^{2}.

$$6x\left(9x^{2}-6x+1\right)+2x^{2}\left(1-3x\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 6x b'9x^{2}-6x+1.

$$54x^{3}-36x^{2}+6x+2x^{2}\left(1-3x\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(1-3x\right)^{2}.

$$54x^{3}-36x^{2}+6x+2x^{2}\left(1-6x+9x^{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x^{2} b'1-6x+9x^{2}.

$$54x^{3}-36x^{2}+6x+2x^{2}-12x^{3}+18x^{4}$$

Ikkombina -36x^{2} u 2x^{2} biex tikseb -34x^{2}.

$$54x^{3}-34x^{2}+6x-12x^{3}+18x^{4}$$

Ikkombina 54x^{3} u -12x^{3} biex tikseb 42x^{3}.

$$42x^{3}-34x^{2}+6x+18x^{4}$$