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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2p+3q\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 4 b'4p^{2}+12pq+9q^{2}.

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(3p-q\right)^{2}.

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

Biex issib l-oppost ta' 9p^{2}-6pq+q^{2}, sib l-oppost ta' kull terminu.

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

Ikkombina 16p^{2} u -9p^{2} biex tikseb 7p^{2}.

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

Ikkombina 48pq u 6pq biex tikseb 54pq.

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

Ikkombina 36q^{2} u -q^{2} biex tikseb 35q^{2}.

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

Espandi

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2p+3q\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 4 b'4p^{2}+12pq+9q^{2}.

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(3p-q\right)^{2}.

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

Biex issib l-oppost ta' 9p^{2}-6pq+q^{2}, sib l-oppost ta' kull terminu.

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

Ikkombina 16p^{2} u -9p^{2} biex tikseb 7p^{2}.

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

Ikkombina 48pq u 6pq biex tikseb 54pq.

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

Ikkombina 36q^{2} u -q^{2} biex tikseb 35q^{2}.

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