a) ![(7\cdot m^{6}+4)\cdot (7\cdot m^{6}-4)](/tpl/images/1062/6439/2ec8f.png)
b) ![(7\cdot a\cdot b^{8}+1)\cdot (7\cdot a\cdot b^{8}-1)](/tpl/images/1062/6439/71500.png)
c) ![a = 0.7\cdot t^{9}](/tpl/images/1062/6439/c19e9.png)
d) There are two possible answers only considering real coefficients:
(i) ![16\cdot x^{2}-81 = (4\cdot x +9)\cdot (4\cdot x - 9)](/tpl/images/1062/6439/4a306.png)
(ii) ![14\cdot x^{2}-81 =(\sqrt{14}\cdot x+9)\cdot (\sqrt{14}\cdot x - 9)](/tpl/images/1062/6439/d7ba7.png)
e) ![(a^{3}+4)\cdot (a^{3}-4)](/tpl/images/1062/6439/36d46.png)
Step-by-step explanation:
Now we proceed to solve each algebraic equation:
a) Factor ![49\cdot m^{12}-16](/tpl/images/1062/6439/90e53.png)
This binomial is of the form
. In this case, we can rewrite and factor the equation below:
![49\cdot m ^{12}-16](/tpl/images/1062/6439/5b162.png)
![(7\cdot m^{6})^ 2-4^{2}](/tpl/images/1062/6439/bf43d.png)
![(7\cdot m^{6}+4)\cdot (7\cdot m^{6}-4)](/tpl/images/1062/6439/2ec8f.png)
b) Factor ![49\cdot a^{2}\cdot b^{16}-1](/tpl/images/1062/6439/f8f0c.png)
This binomial is of the form
. In this case, we can rewrite and factor the equation below:
![49\cdot a^{2}\cdot b^{16}-1](/tpl/images/1062/6439/f8f0c.png)
![(7\cdot a\cdot b^{8})^{2}-1^{2}](/tpl/images/1062/6439/8b462.png)
![(7\cdot a\cdot b^{8}+1)\cdot (7\cdot a\cdot b^{8}-1)](/tpl/images/1062/6439/71500.png)
c) Nicole is factoring
by using the rule
. What will she use for the value of
?
From this rule we find that
, that is:
![a^{2} = 0.49\cdot t^{18}](/tpl/images/1062/6439/a7c37.png)
![a^{2} = \frac{49}{100}\cdot t^{18}](/tpl/images/1062/6439/a25e8.png)
![a = \frac{7}{10}\cdot t^{9}](/tpl/images/1062/6439/4ccfb.png)
![a = 0.7\cdot t^{9}](/tpl/images/1062/6439/c19e9.png)
d) Which binomial is a difference of squares?
A binomial is a difference of square if and only if
. There are two possible answers only considering real coefficients:
(i) ![16\cdot x^{2}-81 = (4\cdot x +9)\cdot (4\cdot x - 9)](/tpl/images/1062/6439/4a306.png)
(ii) ![14\cdot x^{2}-81 =(\sqrt{14}\cdot x+9)\cdot (\sqrt{14}\cdot x - 9)](/tpl/images/1062/6439/d7ba7.png)
e) Factor ![a^{6}-16](/tpl/images/1062/6439/18b24.png)
This binomial is of the form
. In this case, we can rewrite and factor the equation below:
![a^{6}-16](/tpl/images/1062/6439/18b24.png)
![(a^{3})^{2}-4^{2}](/tpl/images/1062/6439/c2b06.png)
![(a^{3}+4)\cdot (a^{3}-4)](/tpl/images/1062/6439/36d46.png)