Issolvi (2x+1/3)^2-(x-1/2)^2

$$( 2 x + \frac { 1 } { 3 } ) ^ { 2 } - ( x - \frac { 1 } { 2 } ) ^ { 2 }$$

Evalwa

$$3x^{2}+\frac{7x}{3}-\frac{5}{36}$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2x+\frac{1}{3}\right)^{2}.

$$4x^{2}+\frac{4}{3}x+\frac{1}{9}-\left(x-\frac{1}{2}\right)^{2}$$

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

$$4x^{2}+\frac{4}{3}x+\frac{1}{9}-\left(x^{2}-x+\frac{1}{4}\right)$$

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

$$4x^{2}+\frac{4}{3}x+\frac{1}{9}-x^{2}+x-\frac{1}{4}$$

Ikkombina 4x^{2} u -x^{2} biex tikseb 3x^{2}.

$$3x^{2}+\frac{4}{3}x+\frac{1}{9}+x-\frac{1}{4}$$

Ikkombina \frac{4}{3}x u x biex tikseb \frac{7}{3}x.

$$3x^{2}+\frac{7}{3}x+\frac{1}{9}-\frac{1}{4}$$

Naqqas \frac{1}{4} minn \frac{1}{9} biex tikseb -\frac{5}{36}.

$$3x^{2}+\frac{7}{3}x-\frac{5}{36}$$

Espandi

$$3x^{2}+\frac{7x}{3}-\frac{5}{36}$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2x+\frac{1}{3}\right)^{2}.

$$4x^{2}+\frac{4}{3}x+\frac{1}{9}-\left(x-\frac{1}{2}\right)^{2}$$

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

$$4x^{2}+\frac{4}{3}x+\frac{1}{9}-\left(x^{2}-x+\frac{1}{4}\right)$$

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

$$4x^{2}+\frac{4}{3}x+\frac{1}{9}-x^{2}+x-\frac{1}{4}$$

Ikkombina 4x^{2} u -x^{2} biex tikseb 3x^{2}.

$$3x^{2}+\frac{4}{3}x+\frac{1}{9}+x-\frac{1}{4}$$

Ikkombina \frac{4}{3}x u x biex tikseb \frac{7}{3}x.

$$3x^{2}+\frac{7}{3}x+\frac{1}{9}-\frac{1}{4}$$

Naqqas \frac{1}{4} minn \frac{1}{9} biex tikseb -\frac{5}{36}.

$$3x^{2}+\frac{7}{3}x-\frac{5}{36}$$