Issolvi (1/3+x/2)(1/9-x^2/4)(frac{1}{3}-frac{x}{2})

$$( \frac { 1 } { 3 } + \frac { x } { 2 } ) ( \frac { 1 } { 9 } - \frac { x ^ { 2 } } { 4 } ) ( \frac { 1 } { 3 } - \frac { x } { 2 } )$$

Evalwa

$$\frac{\left(4-9x^{2}\right)^{2}}{1296}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3 u 2 huwa 6. Immultiplika \frac{1}{3} b'\frac{2}{2}. Immultiplika \frac{x}{2} b'\frac{3}{3}.

$$\left(\frac{2}{6}+\frac{3x}{6}\right)\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Billi \frac{2}{6} u \frac{3x}{6} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{2+3x}{6}\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 9 u 4 huwa 36. Immultiplika \frac{1}{9} b'\frac{4}{4}. Immultiplika \frac{x^{2}}{4} b'\frac{9}{9}.

$$\frac{2+3x}{6}\left(\frac{4}{36}-\frac{9x^{2}}{36}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Billi \frac{4}{36} u \frac{9x^{2}}{36} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{1}{3}-\frac{x}{2}\right)$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3 u 2 huwa 6. Immultiplika \frac{1}{3} b'\frac{2}{2}. Immultiplika \frac{x}{2} b'\frac{3}{3}.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{2}{6}-\frac{3x}{6}\right)$$

Billi \frac{2}{6} u \frac{3x}{6} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\times \frac{2-3x}{6}$$

Immultiplika \frac{2+3x}{6} b'\frac{4-9x^{2}}{36} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36}\times \frac{2-3x}{6}$$

Immultiplika \frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36} b'\frac{2-3x}{6} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{6\times 36\times 6}$$

Immultiplika 6 u 36 biex tikseb 216.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{216\times 6}$$

Immultiplika 216 u 6 biex tikseb 1296.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{1296}$$

Uża l-propjetà distributtiva biex timmultiplika 2+3x b'4-9x^{2}.

$$\frac{\left(8-18x^{2}+12x-27x^{3}\right)\left(2-3x\right)}{1296}$$

Uża l-propjetà distributtiva biex timmultiplika 8-18x^{2}+12x-27x^{3} b'2-3x u kkombina termini simili.

$$\frac{16-72x^{2}+81x^{4}}{1296}$$

Espandi

$$\frac{x^{4}}{16}-\frac{x^{2}}{18}+\frac{1}{81}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3 u 2 huwa 6. Immultiplika \frac{1}{3} b'\frac{2}{2}. Immultiplika \frac{x}{2} b'\frac{3}{3}.

$$\left(\frac{2}{6}+\frac{3x}{6}\right)\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Billi \frac{2}{6} u \frac{3x}{6} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{2+3x}{6}\left(\frac{1}{9}-\frac{x^{2}}{4}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 9 u 4 huwa 36. Immultiplika \frac{1}{9} b'\frac{4}{4}. Immultiplika \frac{x^{2}}{4} b'\frac{9}{9}.

$$\frac{2+3x}{6}\left(\frac{4}{36}-\frac{9x^{2}}{36}\right)\left(\frac{1}{3}-\frac{x}{2}\right)$$

Billi \frac{4}{36} u \frac{9x^{2}}{36} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{1}{3}-\frac{x}{2}\right)$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3 u 2 huwa 6. Immultiplika \frac{1}{3} b'\frac{2}{2}. Immultiplika \frac{x}{2} b'\frac{3}{3}.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\left(\frac{2}{6}-\frac{3x}{6}\right)$$

Billi \frac{2}{6} u \frac{3x}{6} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{2+3x}{6}\times \frac{4-9x^{2}}{36}\times \frac{2-3x}{6}$$

Immultiplika \frac{2+3x}{6} b'\frac{4-9x^{2}}{36} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36}\times \frac{2-3x}{6}$$

Immultiplika \frac{\left(2+3x\right)\left(4-9x^{2}\right)}{6\times 36} b'\frac{2-3x}{6} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{6\times 36\times 6}$$

Immultiplika 6 u 36 biex tikseb 216.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{216\times 6}$$

Immultiplika 216 u 6 biex tikseb 1296.

$$\frac{\left(2+3x\right)\left(4-9x^{2}\right)\left(2-3x\right)}{1296}$$

Uża l-propjetà distributtiva biex timmultiplika 2+3x b'4-9x^{2}.

$$\frac{\left(8-18x^{2}+12x-27x^{3}\right)\left(2-3x\right)}{1296}$$

Uża l-propjetà distributtiva biex timmultiplika 8-18x^{2}+12x-27x^{3} b'2-3x u kkombina termini simili.

$$\frac{16-72x^{2}+81x^{4}}{1296}$$