Issolvi (a+1+2y)^2-(a-1)(a+1)-(1+2y)^2-2a

$$( a + 1 + 2 y ) ^ { 2 } - ( a - 1 ) ( a + 1 ) - ( 1 + 2 y ) ^ { 2 } - 2 a$$

Evalwa

$$4ay+1$$

Passi tas-Soluzzjonijiet

Ikkwadra a+1+2y.

$$4y^{2}+4ay+4y+a^{2}+2a+1-\left(a-1\right)\left(a+1\right)-\left(1+2y\right)^{2}-2a$$

Ikkunsidra li \left(a-1\right)\left(a+1\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Ikkwadra 1.

$$4y^{2}+4ay+4y+a^{2}+2a+1-\left(a^{2}-1\right)-\left(1+2y\right)^{2}-2a$$

Biex issib l-oppost ta' a^{2}-1, sib l-oppost ta' kull terminu.

$$4y^{2}+4ay+4y+a^{2}+2a+1-a^{2}+1-\left(1+2y\right)^{2}-2a$$

Ikkombina a^{2} u -a^{2} biex tikseb 0.

$$4y^{2}+4ay+4y+2a+1+1-\left(1+2y\right)^{2}-2a$$

Żid 1 u 1 biex tikseb 2.

$$4y^{2}+4ay+4y+2a+2-\left(1+2y\right)^{2}-2a$$

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

$$4y^{2}+4ay+4y+2a+2-\left(1+4y+4y^{2}\right)-2a$$

Biex issib l-oppost ta' 1+4y+4y^{2}, sib l-oppost ta' kull terminu.

$$4y^{2}+4ay+4y+2a+2-1-4y-4y^{2}-2a$$

Naqqas 1 minn 2 biex tikseb 1.

$$4y^{2}+4ay+4y+2a+1-4y-4y^{2}-2a$$

Ikkombina 4y u -4y biex tikseb 0.

$$4y^{2}+4ay+2a+1-4y^{2}-2a$$

Ikkombina 4y^{2} u -4y^{2} biex tikseb 0.

$$4ay+2a+1-2a$$

Ikkombina 2a u -2a biex tikseb 0.

$$4ay+1$$

Espandi

$$4ay+1$$

Passi tas-Soluzzjonijiet

Ikkwadra a+1+2y.

$$4y^{2}+4ay+4y+a^{2}+2a+1-\left(a-1\right)\left(a+1\right)-\left(1+2y\right)^{2}-2a$$

Ikkunsidra li \left(a-1\right)\left(a+1\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Ikkwadra 1.

$$4y^{2}+4ay+4y+a^{2}+2a+1-\left(a^{2}-1\right)-\left(1+2y\right)^{2}-2a$$

Biex issib l-oppost ta' a^{2}-1, sib l-oppost ta' kull terminu.

$$4y^{2}+4ay+4y+a^{2}+2a+1-a^{2}+1-\left(1+2y\right)^{2}-2a$$

Ikkombina a^{2} u -a^{2} biex tikseb 0.

$$4y^{2}+4ay+4y+2a+1+1-\left(1+2y\right)^{2}-2a$$

Żid 1 u 1 biex tikseb 2.

$$4y^{2}+4ay+4y+2a+2-\left(1+2y\right)^{2}-2a$$

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

$$4y^{2}+4ay+4y+2a+2-\left(1+4y+4y^{2}\right)-2a$$

Biex issib l-oppost ta' 1+4y+4y^{2}, sib l-oppost ta' kull terminu.

$$4y^{2}+4ay+4y+2a+2-1-4y-4y^{2}-2a$$

Naqqas 1 minn 2 biex tikseb 1.

$$4y^{2}+4ay+4y+2a+1-4y-4y^{2}-2a$$

Ikkombina 4y u -4y biex tikseb 0.

$$4y^{2}+4ay+2a+1-4y^{2}-2a$$

Ikkombina 4y^{2} u -4y^{2} biex tikseb 0.

$$4ay+2a+1-2a$$

Ikkombina 2a u -2a biex tikseb 0.

$$4ay+1$$