Question

1)(4-3√a)(4+3√a)-4a=2)(5-√2a) (5+√2a)-(4a-20)=​

Answer 1

$(4-3\sqrt{a} ) (4+3\sqrt{a} ) -4a= 16-9a-4a=16-13a$

$(5-\sqrt{2a}) (5+\sqrt{2a} )-(4a-20)=25-2a-4a+20=45-6a$

Answer 2

Let's solve each of these expressions step by step:

1. $(4 - 3\sqrt{a})(4 + 3\sqrt{a}) - 4a$:

This expression is in the form $(a - b)(a + b)$, which is the difference of squares formula, where $a = 4$ and $b = 3\sqrt{a}$:

$(a - b)(a + b) = a^2 - b^2$

So, in our case:

$(4 - 3\sqrt{a})(4 + 3\sqrt{a}) = 4^2 - (3\sqrt{a})^2 = 16 - 9a$

Now, subtracting $4a$:

$16 - 9a - 4a = 16 - 13a$

2. $(5 - \sqrt{2a})(5 + \sqrt{2a}) - (4a - 20)$:

Similarly, this is again in the form $(a - b)(a + b)$, where $a = 5$ and $b = \sqrt{2a}$:

$(a - b)(a + b) = a^2 - b^2$

So, in our case:

$(5 - \sqrt{2a})(5 + \sqrt{2a}) = 5^2 - (\sqrt{2a})^2 = 25 - 2a$

Now, subtracting $4a - 20$:

$25 - 2a - 4a + 20 = 45 - 6a$

So, the simplified expressions are:

1. $16 - 13a$
2. $45 - 6a$