15. Multiplying a polynomial by a monomial

Exercises

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Basic exercises
Applied exercises
Challenging exercises

Multiplying a polynomial by a monomial

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By following normal calculation rules, the expression [[$ 2(3+4) $]], which means the same as [[$ 2 \cdot (3+4) $]], is simplified as follows: [[$ 2(3+4) = 2\cdot 7 = 14 $]].

The same result is arrived at by first multiplying both addendums separately [[$ 2(3+4) = 2\cdot 3 +2 \cdot 4 = 6+8 =14 $]]. If the expression contains variables that prevent the sum in brackets from being simplified, the latter method allows you to remove the brackets.

Multiplying a polynomial by a monomial

Each term in the polynomial is multiplied by the monomial separately. Products are added together with their signs.

[[$ a(b+c) = ab +ac $]]

Examples

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Example 1

Multiply the polynomial by a monomial.

Example 2

Calculate [[$ 2(x + 4) $]]. A rectangle with side lengths of [[$ 2 $]] and [[$ (x + 4) $]] can be used as an aid to deduce the answer. The answer is the same as the the area of the rectangle.

Answer: [[$ 2x + 8 $]]

Example 3

Multiply the polynomials by the monomials.

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