Question

Desenvolva os produtos notáveis

A) (6+x)²



B) (2x+10)²



C) (3-x)²



D) x
( – — )²
3



E) (2x-5) . (2x+5)




F) (x+5) . (X-5)

preciso dos cálculos.​

Answer 1

Usarei o binômio de newton:

$(a+b)^n=\sum\limits_{i=0}^{\mbox{n}}=\binom{n}{i}a^{n-i}b^i$

a) $\sum\limits_{i=0}^{\mbox{2}}\binom{2}{i}6^{2-i}x^i=\binom{2}{1}6^{2-0}x^0+\binom{2}{1}6^{2-1}x^1+\binom{2}{2}6^{2-2}x^2\\=(1.36.1)+(2.6.x)+(1.1.x^2)\\=36+12x+x^2$

b) $\sum\limits_{i=0}^{\mbox{2}}\binom{2}{i}(2x)^{2-i}10^i=\binom{2}{0}(2x)^{2-0}.10^0+\binom{2}{1}(2x)^{2-1}.10^1+\binom{2}{2}(2x)^{2-2}.10^2\\=[1.(2x)^2.1]+[2.(2x)^1.10^1]+[1.(2x)^0.10^2]\\=[1.4x^2.1]+[2.2x.10]+[1.1.100]\\=4x^2+40x+100$

c) $\sum\limits_{i=0}^{\mbox{2}}\binom{2}{i}3^{2-i}x^i=\binom{2}{0}3^{2-0}.x^0-\binom{2}{1}3^{2-1}.x^1+\binom{2}{2}3^{2-2}.x^2\\=(1.3^2.1)-(2.3^1.x^1)+(1.1.x^2)\\=9-6x+x^2$

d) NÃO DÁ PRA VER.

Agora, usarei o produto da soma pela diferença: $(a-b)(a+b)=a^2-b^2$.

e) $(2x)^2-5^2\\4x^2-25$

f) $x^2-5^2\\x^2-25$