Réitigh 4left(2p+3qright)^2-left(3p-qright)^2

$$4 { \left(2p+3q \right) }^{ 2 } - { \left(3p-q \right) }^{ 2 }$$

Luacháil

$$\left(p+7q\right)\left(7p+5q\right)$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(2p+3q\right)^{2} a leathnú.

$$4\left(4p^{2}+12pq+9q^{2}\right)-\left(3p-q\right)^{2}$$

Úsáid an t-airí dáileach chun 4 a mhéadú faoi 4p^{2}+12pq+9q^{2}.

$$16p^{2}+48pq+36q^{2}-\left(3p-q\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(3p-q\right)^{2} a leathnú.

$$16p^{2}+48pq+36q^{2}-\left(9p^{2}-6pq+q^{2}\right)$$

Chun an mhalairt ar 9p^{2}-6pq+q^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$16p^{2}+48pq+36q^{2}-9p^{2}+6pq-q^{2}$$

Comhcheangail 16p^{2} agus -9p^{2} chun 7p^{2} a fháil.

$$7p^{2}+48pq+36q^{2}+6pq-q^{2}$$

Comhcheangail 48pq agus 6pq chun 54pq a fháil.

$$7p^{2}+54pq+36q^{2}-q^{2}$$

Comhcheangail 36q^{2} agus -q^{2} chun 35q^{2} a fháil.

$$7p^{2}+54pq+35q^{2}$$

Fairsingigh

$$7p^{2}+54pq+35q^{2}$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(2p+3q\right)^{2} a leathnú.

$$4\left(4p^{2}+12pq+9q^{2}\right)-\left(3p-q\right)^{2}$$

Úsáid an t-airí dáileach chun 4 a mhéadú faoi 4p^{2}+12pq+9q^{2}.

$$16p^{2}+48pq+36q^{2}-\left(3p-q\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(3p-q\right)^{2} a leathnú.

$$16p^{2}+48pq+36q^{2}-\left(9p^{2}-6pq+q^{2}\right)$$

Chun an mhalairt ar 9p^{2}-6pq+q^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$16p^{2}+48pq+36q^{2}-9p^{2}+6pq-q^{2}$$

Comhcheangail 16p^{2} agus -9p^{2} chun 7p^{2} a fháil.

$$7p^{2}+48pq+36q^{2}+6pq-q^{2}$$

Comhcheangail 48pq agus 6pq chun 54pq a fháil.

$$7p^{2}+54pq+36q^{2}-q^{2}$$

Comhcheangail 36q^{2} agus -q^{2} chun 35q^{2} a fháil.

$$7p^{2}+54pq+35q^{2}$$