The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To multiply terms with radicals, multiply the coefficients and radicands separately:

2\( \sqrt{5} \) x 5\( \sqrt{3} \)
(2 x 5)\( \sqrt{5 \times 3} \)
10\( \sqrt{15} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{7} \) x \( \frac{3}{8} \) = \( \frac{1 x 3}{7 x 8} \) = \( \frac{3}{56} \) = \(\frac{3}{56}\)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (4 + 3) ÷ 2 x 2 - 4²
P: 5 + (7) ÷ 2 x 2 - 4²
E: 5 + 7 ÷ 2 x 2 - 16
MD: 5 + \( \frac{7}{2} \) x 2 - 16
MD: 5 + \( \frac{14}{2} \) - 16
AS: \( \frac{10}{2} \) + \( \frac{14}{2} \) - 16
AS: \( \frac{24}{2} \) - 16
AS: \( \frac{24 - 32}{2} \)
\( \frac{-8}{2} \)
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