Datrys (2a-3b)^2-(b+a)^2

$$( 2 a - 3 b ) ^ { 2 } - ( b + a ) ^ { 2 }$$

Enrhifo

$$\left(a-4b\right)\left(3a-2b\right)$$

Camau Ateb

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

$$4a^{2}-12ab+9b^{2}-\left(b+a\right)^{2}$$

Defnyddio'r theorem binomaidd \left(p+q\right)^{2}=p^{2}+2pq+q^{2} i ehangu'r \left(b+a\right)^{2}.

$$4a^{2}-12ab+9b^{2}-\left(b^{2}+2ba+a^{2}\right)$$

I ddod o hyd i wrthwyneb b^{2}+2ba+a^{2}, dewch o hyd i wrthwyneb pob term.

$$4a^{2}-12ab+9b^{2}-b^{2}-2ba-a^{2}$$

Cyfuno 9b^{2} a -b^{2} i gael 8b^{2}.

$$4a^{2}-12ab+8b^{2}-2ba-a^{2}$$

Cyfuno -12ab a -2ba i gael -14ab.

$$4a^{2}-14ab+8b^{2}-a^{2}$$

Cyfuno 4a^{2} a -a^{2} i gael 3a^{2}.

$$3a^{2}-14ab+8b^{2}$$

Ehangu

$$3a^{2}-14ab+8b^{2}$$

Camau Ateb

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

$$4a^{2}-12ab+9b^{2}-\left(b+a\right)^{2}$$

Defnyddio'r theorem binomaidd \left(p+q\right)^{2}=p^{2}+2pq+q^{2} i ehangu'r \left(b+a\right)^{2}.

$$4a^{2}-12ab+9b^{2}-\left(b^{2}+2ba+a^{2}\right)$$

I ddod o hyd i wrthwyneb b^{2}+2ba+a^{2}, dewch o hyd i wrthwyneb pob term.

$$4a^{2}-12ab+9b^{2}-b^{2}-2ba-a^{2}$$

Cyfuno 9b^{2} a -b^{2} i gael 8b^{2}.

$$4a^{2}-12ab+8b^{2}-2ba-a^{2}$$

Cyfuno -12ab a -2ba i gael -14ab.

$$4a^{2}-14ab+8b^{2}-a^{2}$$

Cyfuno 4a^{2} a -a^{2} i gael 3a^{2}.

$$3a^{2}-14ab+8b^{2}$$