Issolvi (a+y-2)(a+y+2)-(a-y)^2-4(ay-1)+1

$$( a + y - 2 ) ( a + y + 2 ) - ( a - y ) ^ { 2 } - 4 ( a y - 1 ) + 1$$

Evalwa

$$1$$

Passi tas-Soluzzjonijiet

Ikkunsidra li \left(a+y-2\right)\left(a+y+2\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}, fejn a=a+y u b=2. Ikkwadra 2.

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

Uża teorema binomjali \left(p+q\right)^{2}=p^{2}+2pq+q^{2} biex tespandi \left(a+y\right)^{2}.

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

Uża teorema binomjali \left(p-q\right)^{2}=p^{2}-2pq+q^{2} biex tespandi \left(a-y\right)^{2}.

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

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

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

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

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

Ikkombina 2ay u 2ay biex tikseb 4ay.

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

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

$$4ay-4-4\left(ay-1\right)+1$$

Uża l-propjetà distributtiva biex timmultiplika -4 b'ay-1.

$$4ay-4-4ay+4+1$$

Ikkombina 4ay u -4ay biex tikseb 0.

$$-4+4+1$$

Żid -4 u 4 biex tikseb 0.

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Fattur

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