Issolvi (25p-15q)^2-(15p-25q)^2

$$( 25 p - 15 q ) ^ { 2 } - ( 15 p - 25 q ) ^ { 2 }$$

Evalwa

$$400\left(p^{2}-q^{2}\right)$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(25p-15q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(15p-25q\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(15p-25q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(225p^{2}-750pq+625q^{2}\right)$$

Biex issib l-oppost ta' 225p^{2}-750pq+625q^{2}, sib l-oppost ta' kull terminu.

$$625p^{2}-750pq+225q^{2}-225p^{2}+750pq-625q^{2}$$

Ikkombina 625p^{2} u -225p^{2} biex tikseb 400p^{2}.

$$400p^{2}-750pq+225q^{2}+750pq-625q^{2}$$

Ikkombina -750pq u 750pq biex tikseb 0.

$$400p^{2}+225q^{2}-625q^{2}$$

Ikkombina 225q^{2} u -625q^{2} biex tikseb -400q^{2}.

$$400p^{2}-400q^{2}$$

Espandi

$$400p^{2}-400q^{2}$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(25p-15q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(15p-25q\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(15p-25q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(225p^{2}-750pq+625q^{2}\right)$$

Biex issib l-oppost ta' 225p^{2}-750pq+625q^{2}, sib l-oppost ta' kull terminu.

$$625p^{2}-750pq+225q^{2}-225p^{2}+750pq-625q^{2}$$

Ikkombina 625p^{2} u -225p^{2} biex tikseb 400p^{2}.

$$400p^{2}-750pq+225q^{2}+750pq-625q^{2}$$

Ikkombina -750pq u 750pq biex tikseb 0.

$$400p^{2}+225q^{2}-625q^{2}$$

Ikkombina 225q^{2} u -625q^{2} biex tikseb -400q^{2}.

$$400p^{2}-400q^{2}$$