Issolvi (2)(3x+y)^2-(x-5y)^2

$$( 2 ) ( 3 x + y ) ^ { 2 } - ( x - 5 y ) ^ { 2 }$$

Evalwa

$$17x^{2}+22xy-23y^{2}$$

Passi tas-Soluzzjonijiet

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

$$2\left(9x^{2}+6xy+y^{2}\right)-\left(x-5y\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'9x^{2}+6xy+y^{2}.

$$18x^{2}+12xy+2y^{2}-\left(x-5y\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-5y\right)^{2}.

$$18x^{2}+12xy+2y^{2}-\left(x^{2}-10xy+25y^{2}\right)$$

Biex issib l-oppost ta' x^{2}-10xy+25y^{2}, sib l-oppost ta' kull terminu.

$$18x^{2}+12xy+2y^{2}-x^{2}+10xy-25y^{2}$$

Ikkombina 18x^{2} u -x^{2} biex tikseb 17x^{2}.

$$17x^{2}+12xy+2y^{2}+10xy-25y^{2}$$

Ikkombina 12xy u 10xy biex tikseb 22xy.

$$17x^{2}+22xy+2y^{2}-25y^{2}$$

Ikkombina 2y^{2} u -25y^{2} biex tikseb -23y^{2}.

$$17x^{2}+22xy-23y^{2}$$

Espandi

$$17x^{2}+22xy-23y^{2}$$

Passi tas-Soluzzjonijiet

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

$$2\left(9x^{2}+6xy+y^{2}\right)-\left(x-5y\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'9x^{2}+6xy+y^{2}.

$$18x^{2}+12xy+2y^{2}-\left(x-5y\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-5y\right)^{2}.

$$18x^{2}+12xy+2y^{2}-\left(x^{2}-10xy+25y^{2}\right)$$

Biex issib l-oppost ta' x^{2}-10xy+25y^{2}, sib l-oppost ta' kull terminu.

$$18x^{2}+12xy+2y^{2}-x^{2}+10xy-25y^{2}$$

Ikkombina 18x^{2} u -x^{2} biex tikseb 17x^{2}.

$$17x^{2}+12xy+2y^{2}+10xy-25y^{2}$$

Ikkombina 12xy u 10xy biex tikseb 22xy.

$$17x^{2}+22xy+2y^{2}-25y^{2}$$

Ikkombina 2y^{2} u -25y^{2} biex tikseb -23y^{2}.

$$17x^{2}+22xy-23y^{2}$$