multiply the conjugates
(2a+5b)(2a-5b)
Using the FOIL method (First, Outer, Inner, Last), we can expand the expression:
(2a + 5b)(2a - 5b)
= (2a)(2a) + (2a)(-5b) + (5b)(2a) + (5b)(-5b)
= 4a^2 - 10ab + 10ab - 25b^2
= 4a^2 - 25b^2
Therefore, the expression (2a + 5b)(2a - 5b) simplifies to 4a^2 - 25b^2.
multiply the conjugates
(2/3r-6)(2/3r+6)
apply the formula (a-b)(a+b)=a^2-b^2
Using the formula (a - b)(a + b) = a^2 - b^2, we can simplify the expression:
(2/3r - 6)(2/3r + 6)
= (2/3r)^2 - 6^2
= (4/9r^2) - 36/1
= 4/9r^2 - 36
Therefore, the expression (2/3r - 6)(2/3r + 6) simplifies to 4/9r^2 - 36.
multiply the conjugates
(3/5-q)(3/5+q)
To calculate the product of the conjugates, we can use the formula (a - b)(a + b) = a^2 - b^2.
In this case, a = 3/5 and b = q, so we have:
(3/5 - q)(3/5 + q) = (3/5)^2 - q^2 = 9/25 - q^2.
Therefore, the expression (3/5 - q)(3/5 + q) simplifies to 9/25 - q^2.
To multiply the conjugates (2a+5b)(2a-5b), you can use the FOIL method. FOIL stands for First, Outer, Inner, Last. Here's how you do it:
First - Multiply the first terms of each binomial:
(2a)*(2a) = 4a^2
Outer - Multiply the outer terms of each binomial:
(2a)*(-5b) = -10ab
Inner - Multiply the inner terms of each binomial:
(5b)*(2a) = 10ab
Last - Multiply the last terms of each binomial:
(5b)*(-5b) = -25b^2
Now, you can add up the four terms you obtained:
4a^2 - 10ab + 10ab - 25b^2
Notice that the middle terms, -10ab and 10ab, cancel each other out. This is because they are like terms with opposite signs.
Simplifying further, you get:
4a^2 - 25b^2
So, the product of the conjugates (2a+5b)(2a-5b) is 4a^2 - 25b^2.