Issolvi (a+b)^2-[(a-b)^2+(a+b)(a-b)-4a(a-b)]-(3a^2+b^2)

$$( a + b ) ^ { 2 } - [ ( a - b ) ^ { 2 } + ( a + b ) ( a - b ) - 4 a ( a - b ) ] - ( 3 a ^ { 2 } + b ^ { 2 } )$$

Evalwa

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Passi tas-Soluzzjonijiet

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

$$a^{2}+2ab+b^{2}-\left(\left(a-b\right)^{2}+\left(a+b\right)\left(a-b\right)-4a\left(a-b\right)\right)-\left(3a^{2}+b^{2}\right)$$

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

$$a^{2}+2ab+b^{2}-\left(a^{2}-2ab+b^{2}+\left(a+b\right)\left(a-b\right)-4a\left(a-b\right)\right)-\left(3a^{2}+b^{2}\right)$$

Ikkunsidra li \left(a+b\right)\left(a-b\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}.

$$a^{2}+2ab+b^{2}-\left(a^{2}-2ab+b^{2}+a^{2}-b^{2}-4a\left(a-b\right)\right)-\left(3a^{2}+b^{2}\right)$$

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

$$a^{2}+2ab+b^{2}-\left(2a^{2}-2ab+b^{2}-b^{2}-4a\left(a-b\right)\right)-\left(3a^{2}+b^{2}\right)$$

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

$$a^{2}+2ab+b^{2}-\left(2a^{2}-2ab-4a\left(a-b\right)\right)-\left(3a^{2}+b^{2}\right)$$

Biex issib l-oppost ta' 3a^{2}+b^{2}, sib l-oppost ta' kull terminu.

$$a^{2}+2ab+b^{2}-\left(2a^{2}-2ab-4a\left(a-b\right)\right)-3a^{2}-b^{2}$$

Uża l-propjetà distributtiva biex timmultiplika -4a b'a-b.

$$a^{2}+2ab+b^{2}-\left(2a^{2}-2ab-4a^{2}+4ab\right)-3a^{2}-b^{2}$$

Ikkombina 2a^{2} u -4a^{2} biex tikseb -2a^{2}.

$$a^{2}+2ab+b^{2}-\left(-2a^{2}-2ab+4ab\right)-3a^{2}-b^{2}$$

Ikkombina -2ab u 4ab biex tikseb 2ab.

$$a^{2}+2ab+b^{2}-\left(-2a^{2}+2ab\right)-3a^{2}-b^{2}$$

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

$$a^{2}+2ab+b^{2}+2a^{2}-2ab-3a^{2}-b^{2}$$

Ikkombina a^{2} u 2a^{2} biex tikseb 3a^{2}.

$$3a^{2}+2ab+b^{2}-2ab-3a^{2}-b^{2}$$

Ikkombina 2ab u -2ab biex tikseb 0.

$$3a^{2}+b^{2}-3a^{2}-b^{2}$$

Ikkombina 3a^{2} u -3a^{2} biex tikseb 0.

$$b^{2}-b^{2}$$

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

$$0$$

Fattur

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