Issolvi (x+5)^2+2(x+5)(y-1)+(y-1)^2

$$( x + 5 ) ^ { 2 } + 2 ( x + 5 ) ( y - 1 ) + ( y - 1 ) ^ { 2 }$$

Evalwa

$$\left(x+y+4\right)^{2}$$

Passi tas-Soluzzjonijiet

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

$$x^{2}+10x+25+2\left(x+5\right)\left(y-1\right)+\left(y-1\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'x+5.

$$x^{2}+10x+25+\left(2x+10\right)\left(y-1\right)+\left(y-1\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 2x+10 b'y-1.

$$x^{2}+10x+25+2xy-2x+10y-10+\left(y-1\right)^{2}$$

Ikkombina 10x u -2x biex tikseb 8x.

$$x^{2}+8x+25+2xy+10y-10+\left(y-1\right)^{2}$$

Naqqas 10 minn 25 biex tikseb 15.

$$x^{2}+8x+15+2xy+10y+\left(y-1\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(y-1\right)^{2}.

$$x^{2}+8x+15+2xy+10y+y^{2}-2y+1$$

Ikkombina 10y u -2y biex tikseb 8y.

$$x^{2}+8x+15+2xy+8y+y^{2}+1$$

Żid 15 u 1 biex tikseb 16.

$$x^{2}+8x+16+2xy+8y+y^{2}$$

Espandi

$$x^{2}+2xy+8x+y^{2}+8y+16$$

Passi tas-Soluzzjonijiet

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

$$x^{2}+10x+25+2\left(x+5\right)\left(y-1\right)+\left(y-1\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'x+5.

$$x^{2}+10x+25+\left(2x+10\right)\left(y-1\right)+\left(y-1\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 2x+10 b'y-1.

$$x^{2}+10x+25+2xy-2x+10y-10+\left(y-1\right)^{2}$$

Ikkombina 10x u -2x biex tikseb 8x.

$$x^{2}+8x+25+2xy+10y-10+\left(y-1\right)^{2}$$

Naqqas 10 minn 25 biex tikseb 15.

$$x^{2}+8x+15+2xy+10y+\left(y-1\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(y-1\right)^{2}.

$$x^{2}+8x+15+2xy+10y+y^{2}-2y+1$$

Ikkombina 10y u -2y biex tikseb 8y.

$$x^{2}+8x+15+2xy+8y+y^{2}+1$$

Żid 15 u 1 biex tikseb 16.

$$x^{2}+8x+16+2xy+8y+y^{2}$$