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

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

Arvuta

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

Lahenduse etapid

Kasutage kaksliikme \left(25p-15q\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

Kasutage kaksliikme \left(15p-25q\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

Avaldise "225p^{2}-750pq+625q^{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Kombineerige 625p^{2} ja -225p^{2}, et leida 400p^{2}.

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

Kombineerige -750pq ja 750pq, et leida 0.

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

Kombineerige 225q^{2} ja -625q^{2}, et leida -400q^{2}.

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

Laienda

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

Lahenduse etapid

Kasutage kaksliikme \left(25p-15q\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

Kasutage kaksliikme \left(15p-25q\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

Avaldise "225p^{2}-750pq+625q^{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Kombineerige 625p^{2} ja -225p^{2}, et leida 400p^{2}.

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

Kombineerige -750pq ja 750pq, et leida 0.

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

Kombineerige 225q^{2} ja -625q^{2}, et leida -400q^{2}.

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