Datrys f(x)=-(x-2)(x+1)^2(x-3)^2

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

Enrhifo

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

Camau Ateb

I ddod o hyd i wrthwyneb x-2, dewch o hyd i wrthwyneb pob term.

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

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(x+1\right)^{2}.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(x-3\right)^{2}.

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

Defnyddio’r briodwedd ddosbarthu i luosi -x+2 â x^{2}+2x+1 a chyfuno termau tebyg.

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

Defnyddio’r briodwedd ddosbarthu i luosi -x^{3}+3x+2 â x^{2}-6x+9 a chyfuno termau tebyg.

$$-x^{5}+6x^{4}-6x^{3}-16x^{2}+15x+18$$

Ehangu

$$18+15x-16x^{2}-6x^{3}+6x^{4}-x^{5}$$

Camau Ateb

I ddod o hyd i wrthwyneb x-2, dewch o hyd i wrthwyneb pob term.

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

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(x+1\right)^{2}.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(x-3\right)^{2}.

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

Defnyddio’r briodwedd ddosbarthu i luosi -x+2 â x^{2}+2x+1 a chyfuno termau tebyg.

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

Defnyddio’r briodwedd ddosbarthu i luosi -x^{3}+3x+2 â x^{2}-6x+9 a chyfuno termau tebyg.

$$-x^{5}+6x^{4}-6x^{3}-16x^{2}+15x+18$$