Issolvi (x+3)^2-(6+x)(x-6)-(1-x)^2+x(x-8)

$$( x + 3 ) ^ { 2 } - ( 6 + x ) ( x - 6 ) - ( 1 - x ) ^ { 2 } + x ( x - 8 )$$

Evalwa

$$44$$

Passi tas-Soluzzjonijiet

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

$$x^{2}+6x+9-\left(6+x\right)\left(x-6\right)-\left(1-x\right)^{2}+x\left(x-8\right)$$

Uża l-propjetà distributtiva biex timmultiplika 6+x b'x-6 u kkombina termini simili.

$$x^{2}+6x+9-\left(-36+x^{2}\right)-\left(1-x\right)^{2}+x\left(x-8\right)$$

Biex issib l-oppost ta' -36+x^{2}, sib l-oppost ta' kull terminu.

$$x^{2}+6x+9+36-x^{2}-\left(1-x\right)^{2}+x\left(x-8\right)$$

Żid 9 u 36 biex tikseb 45.

$$x^{2}+6x+45-x^{2}-\left(1-x\right)^{2}+x\left(x-8\right)$$

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

$$6x+45-\left(1-x\right)^{2}+x\left(x-8\right)$$

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

$$6x+45-\left(1-2x+x^{2}\right)+x\left(x-8\right)$$

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

$$6x+45-1+2x-x^{2}+x\left(x-8\right)$$

Naqqas 1 minn 45 biex tikseb 44.

$$6x+44+2x-x^{2}+x\left(x-8\right)$$

Ikkombina 6x u 2x biex tikseb 8x.

$$8x+44-x^{2}+x\left(x-8\right)$$

Uża l-propjetà distributtiva biex timmultiplika x b'x-8.

$$8x+44-x^{2}+x^{2}-8x$$

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

$$8x+44-8x$$

Ikkombina 8x u -8x biex tikseb 0.

$$44$$

Fattur

$$2^{2}\times 11$$