Answer :
Let's solve the problem step by step.
We need to multiply the binomials [tex]\((\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})\)[/tex].
This expression takes the form of a difference of squares, which allows us to use the formula:
[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]
Here, we have:
[tex]\[ a = \sqrt{10} \][/tex]
[tex]\[ b = 2\sqrt{8} \][/tex]
First, let's calculate [tex]\(a^2\)[/tex]:
[tex]\[ a^2 = (\sqrt{10})^2 = 10 \][/tex]
Next, let's calculate [tex]\(b^2\)[/tex]:
[tex]\[ b = 2\sqrt{8} \rightarrow b^2 = (2\sqrt{8})^2 = 4 \times 8 = 32 \][/tex]
Using the difference of squares formula, we now compute:
[tex]\[ (\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = a^2 - b^2 = 10 - 32 = -22 \][/tex]
Thus, the result of the multiplication is:
[tex]\[ -22 \][/tex]
We need to multiply the binomials [tex]\((\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})\)[/tex].
This expression takes the form of a difference of squares, which allows us to use the formula:
[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]
Here, we have:
[tex]\[ a = \sqrt{10} \][/tex]
[tex]\[ b = 2\sqrt{8} \][/tex]
First, let's calculate [tex]\(a^2\)[/tex]:
[tex]\[ a^2 = (\sqrt{10})^2 = 10 \][/tex]
Next, let's calculate [tex]\(b^2\)[/tex]:
[tex]\[ b = 2\sqrt{8} \rightarrow b^2 = (2\sqrt{8})^2 = 4 \times 8 = 32 \][/tex]
Using the difference of squares formula, we now compute:
[tex]\[ (\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = a^2 - b^2 = 10 - 32 = -22 \][/tex]
Thus, the result of the multiplication is:
[tex]\[ -22 \][/tex]
