Question

7.3 multiplying polynomials quiz

when multiplying polynomials, each term must be multiplied by every term.

true
false

Explanation:

Analyze the statement

Using the Distributive Property knowledge point

The statement says: "When multiplying polynomials, each term must be multiplied by every term." In algebra, multiplying two polynomials requires applying the distributive property systematically. Specifically, every term in the first polynomial must be multiplied by every term in the second polynomial.

Verify with an algebraic example

Using the Simplifying Polynomials knowledge point

Consider multiplying two binomials:

$$ (a + b)(c + d) $$

Applying the distributive property:

$$ (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd $$

Each of the 2 terms in the first polynomial is multiplied by each of the 2 terms in the second polynomial, resulting in \(2 \times 2 = 4\) individual product terms before simplification.

Evaluate the truth value

Since the distributive property requires every term of the first polynomial to be multiplied by every term of the second polynomial, the statement is mathematically correct. Therefore, the correct option is True.

Answer:

• True (Correct answer)
• False