Question

How do you factor \[8x - 20\]?

Answer 1

Hint: Here, we will first rewrite each term of the given expression as a product of two numbers. Then we will use the distributive law of multiplication to factor the given algebraic expression by factoring the common factors.

Formula used:
The distributive law of multiplication states that \[a \cdot b + a \cdot c = a\left( {b + c} \right)\].

Complete step-by-step solution:
The coefficient of \[x\] in the given expression is 8, and the constant is 20.
The factors of the number 8 are 1, 2, 4, 8.
The factors of the number 20 are 1, 2, 4, 5, 10, 20.
The numbers 8 and 20 have common factors 1, 2, 4.
Since 1 and 2 are factors of 4, we can factor out 4 from the given expression to get the factored expression.
Rewriting 8 as the product of 4 and 2, and 20 as the product of 4 and 5, we get
\[ \Rightarrow 8x - 20 = 4 \cdot 2x - 4 \cdot 5\]
The distributive law of multiplication states that \[a \cdot b + a \cdot c = a\left( {b + c} \right)\].
Factoring the expression using the distributive law of multiplication, we get
\[ \Rightarrow 8x - 20 = 4\left( {2x - 5} \right)\]
The numbers \[2x\] and 5 have no common factor other than 1.
Therefore, we cannot factorize the expression further.

Thus, we can factor the algebraic expression \[8x - 20\] as \[4\left( {2x - 5} \right)\].

Note:
We can verify our factorization by multiplying the factors using the distributive law of multiplication.
If the expression obtained is \[8x - 20\], then our answer is verified.
The distributive law of multiplication states that \[a\left( {b + c} \right) = a \cdot b + a \cdot c\].
Multiplying 4 by \[2x - 5\] using the distributive law of multiplication, we get
\[4\left( {2x - 5} \right) = 4 \cdot 2x - 4 \cdot 5\]
Multiplying the terms in the expression, we get
\[ \Rightarrow 4\left( {2x - 5} \right) = 8x - 20\]
Since multiplying the factors gives the product as the expression \[8x - 20\], we have verified our answer.
Thus, the algebraic expression \[8x - 20\] can be factored as \[4\left( {2x - 5} \right)\].