Issolvi left(5x-2right)^2-left(3x+1right)^2-x^2-60

$${ \left(5x-2 \right) }^{ 2 } - { \left(3x+1 \right) }^{ 2 } - { x }^{ 2 } -60$$

Evalwa

$$\left(x-3\right)\left(15x+19\right)$$

Passi tas-Soluzzjonijiet

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

$$25x^{2}-20x+4-\left(3x+1\right)^{2}-x^{2}-60$$

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

$$25x^{2}-20x+4-\left(9x^{2}+6x+1\right)-x^{2}-60$$

Biex issib l-oppost ta' 9x^{2}+6x+1, sib l-oppost ta' kull terminu.

$$25x^{2}-20x+4-9x^{2}-6x-1-x^{2}-60$$

Ikkombina 25x^{2} u -9x^{2} biex tikseb 16x^{2}.

$$16x^{2}-20x+4-6x-1-x^{2}-60$$

Ikkombina -20x u -6x biex tikseb -26x.

$$16x^{2}-26x+4-1-x^{2}-60$$

Naqqas 1 minn 4 biex tikseb 3.

$$16x^{2}-26x+3-x^{2}-60$$

Ikkombina 16x^{2} u -x^{2} biex tikseb 15x^{2}.

$$15x^{2}-26x+3-60$$

Naqqas 60 minn 3 biex tikseb -57.

$$15x^{2}-26x-57$$

Espandi

$$15x^{2}-26x-57$$

Passi tas-Soluzzjonijiet

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

$$25x^{2}-20x+4-\left(3x+1\right)^{2}-x^{2}-60$$

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

$$25x^{2}-20x+4-\left(9x^{2}+6x+1\right)-x^{2}-60$$

Biex issib l-oppost ta' 9x^{2}+6x+1, sib l-oppost ta' kull terminu.

$$25x^{2}-20x+4-9x^{2}-6x-1-x^{2}-60$$

Ikkombina 25x^{2} u -9x^{2} biex tikseb 16x^{2}.

$$16x^{2}-20x+4-6x-1-x^{2}-60$$

Ikkombina -20x u -6x biex tikseb -26x.

$$16x^{2}-26x+4-1-x^{2}-60$$

Naqqas 1 minn 4 biex tikseb 3.

$$16x^{2}-26x+3-x^{2}-60$$

Ikkombina 16x^{2} u -x^{2} biex tikseb 15x^{2}.

$$15x^{2}-26x+3-60$$

Naqqas 60 minn 3 biex tikseb -57.

$$15x^{2}-26x-57$$