Løs =w^2005^2+(1-w)^2008^2+2w(1-w)*03*005*008

$$= w ^ { 2 } 005 ^ { 2 } + ( 1 - w ) ^ { 2 } 008 ^ { 2 } + 2 w ( 1 - w ) \times 03 \times 005 \times 008$$

Evaluer

$$\text{Indeterminate}$$

Løsningsvejledning

Multiplicer 0 og 0 for at få 0.

$$w^{2}\times 0\times 5^{2}+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Beregn 5 til potensen af 2, og få 25.

$$w^{2}\times 0\times 25+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiplicer 0 og 25 for at få 0.

$$w^{2}\times 0+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Ethvert tal gange nul giver nul.

$$0+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Brug binomialsætningen \left(a-b\right)^{2}=a^{2}-2ab+b^{2} til at udvide \left(1-w\right)^{2}.

$$0+\left(1-2w+w^{2}\right)\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiplicer 0 og 0 for at få 0.

$$0+\left(1-2w+w^{2}\right)\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Beregn 8 til potensen af 2, og få 64.

$$0+\left(1-2w+w^{2}\right)\times 0\times 64+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiplicer 0 og 64 for at få 0.

$$0+\left(1-2w+w^{2}\right)\times 0+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Ethvert tal gange nul giver nul.

$$0+0+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Tilføj 0 og 0 for at få 0.

$$2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiplicer 2 og 0 for at få 0.

$$0w\left(1-w\right)\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiplicer 0 og 3 for at få 0.

$$0w\left(1-w\right)\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiplicer 0 og 0 for at få 0.

$$0w\left(1-w\right)\times 0\times 5\times 0\times 0\times 8$$

Multiplicer 0 og 0 for at få 0.

$$0w\left(1-w\right)\times 5\times 0\times 0\times 8$$

Multiplicer 0 og 5 for at få 0.

$$0w\left(1-w\right)\times 0\times 0\times 8$$

Multiplicer 0 og 0 for at få 0.

$$0w\left(1-w\right)\times 0\times 8$$

Multiplicer 0 og 0 for at få 0.

$$0w\left(1-w\right)\times 8$$

Multiplicer 0 og 8 for at få 0.

$$0w\left(1-w\right)$$

Ethvert tal gange nul giver nul.

$$0$$