The equivalent expression of the binomial expression \(9x+21\) is \(\boxed{3(3x+7)}\).
Further explanation:
The distributive property of multiplication over addition can be expressed as follows,
\(a(b+c)\)
Here, \(a,b\;\text{and}\;c\) are the real numbers.
The binomial expression is the expression that involves the two terms of the polynomial.
Therefore, the expression \(b+c\) is the binomial expression.
Given:
The given expression is \(9x+21\).
Step by step explanation:
Step 1:
The expression is \(9x+21\).
The given expression is the binomial expression as it includes two terms \(9x\;\text{and}\;21\).
First we factorize the terms of the given binomial expression as,
\(9x = 3 \cdot 3x{\text{ and 21}} = 3 \cdot 7\)
Step 2:
Now the given expression can be written in the factorized form as,
\(9x + 21 = 3 \cdot 3x + 3 \cdot 7\)
Step 3:
Now take greatest common factor 3 by the use of parenthesis from the resultant expression.
\(3 \cdot 3x + 3 \cdot 7 = 3\left( {3x + 7} \right)\)
Therefore, it can be seen that the resultant expression \(3\left( {3x + 7} \right)\) is an equivalent expression of the given binomial expression \(9x + 21\).
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Answer details:
Grade: Juniorschool
Subject: Mathematics
Chapter: Arithmetic properties of real numbers.
Keywords: Real numbers, binomial expression, distributive property, multiplication, addition, greatest common factor, simplification, parenthesis, operation, arithmetic properties
