Issolvi 49(a-b)^2-16(a+b)^2

$$49 ( a - b ) ^ { 2 } - 16 ( a + b ) ^ { 2 }$$

Evalwa

$$\left(3a-11b\right)\left(11a-3b\right)$$

Passi tas-Soluzzjonijiet

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

$$49\left(a^{2}-2ab+b^{2}\right)-16\left(a+b\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 49 b'a^{2}-2ab+b^{2}.

$$49a^{2}-98ab+49b^{2}-16\left(a+b\right)^{2}$$

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

$$49a^{2}-98ab+49b^{2}-16\left(a^{2}+2ab+b^{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika -16 b'a^{2}+2ab+b^{2}.

$$49a^{2}-98ab+49b^{2}-16a^{2}-32ab-16b^{2}$$

Ikkombina 49a^{2} u -16a^{2} biex tikseb 33a^{2}.

$$33a^{2}-98ab+49b^{2}-32ab-16b^{2}$$

Ikkombina -98ab u -32ab biex tikseb -130ab.

$$33a^{2}-130ab+49b^{2}-16b^{2}$$

Ikkombina 49b^{2} u -16b^{2} biex tikseb 33b^{2}.

$$33a^{2}-130ab+33b^{2}$$

Espandi

$$33a^{2}-130ab+33b^{2}$$

Passi tas-Soluzzjonijiet

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

$$49\left(a^{2}-2ab+b^{2}\right)-16\left(a+b\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 49 b'a^{2}-2ab+b^{2}.

$$49a^{2}-98ab+49b^{2}-16\left(a+b\right)^{2}$$

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

$$49a^{2}-98ab+49b^{2}-16\left(a^{2}+2ab+b^{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika -16 b'a^{2}+2ab+b^{2}.

$$49a^{2}-98ab+49b^{2}-16a^{2}-32ab-16b^{2}$$

Ikkombina 49a^{2} u -16a^{2} biex tikseb 33a^{2}.

$$33a^{2}-98ab+49b^{2}-32ab-16b^{2}$$

Ikkombina -98ab u -32ab biex tikseb -130ab.

$$33a^{2}-130ab+49b^{2}-16b^{2}$$

Ikkombina 49b^{2} u -16b^{2} biex tikseb 33b^{2}.

$$33a^{2}-130ab+33b^{2}$$