The answer is: " 3(m − 2) " .
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→ The "factorized version" of the binomial expression, " 3m − 6 " , is:
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→ " 3(m − 2) " .
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Explanation:
To solve:
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<u>Note</u>: We are given the expression: " 3m − 6 " ;
and we are asked to "factorize" this expression.
Note that this expression is a "binomial expression" — which means there are two (2) terms — in this case: "3m" and "6" .
Since only one (1) of these 2 (two) terms has a variable, and the remaining terms is a "constant" (non-zero integer), write these 2 (two) terms as:
1) the coefficient of the variable given in the term shown with a "coefficient" :
→ that is: "3" ; and:
2) the other term: "6" .
→ With the numbers: "3 and 6" , we can factor out a "3" ;
→ {since: " 6 ÷ 3 = 2 "} ;
→ So; given:
" 3m − 6 " ;
→ We can "factor out" a "3" ; as follows:
→ Take the first term: " 3m " :
" 3m = 3 * m " ;
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→ Take the second term: " 6 " :
" 6 = 3 * (what value?) ;
→ divide each of this equation by "3" ;
to isolate the "missing value" on one side of the equation; & to solve for the "missing value" ; as follows:
→ " 6 / 3 = [ 3 * (what value?) ] / 3 ;
→ to get: " 2 = "(the missing value)" ;
→ So; " 6 = 3 * (what value?) ;
→ " 6 = 3 * 2 " .
→ Take the second term: " 6 " :
→ " 6 = 3 * 2 " .
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So: " 3m − 6 " = (3 * m) − (3 * 2) " .
Factor out a "3" ; as follows:
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→ " 3m − 6 " = (3 * m) − (3 * 2) " ;
= " 3(m − 2) "
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Let us check our answer:
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ;
a(b − c) = ab − ac ;
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So: Take our answer: " 3(m − 2) " .
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" 3(m − 2) = ? (3*m) − (3*2) " ?? ;
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Let us substitute "4" for "m" ; in both sides of the equation;
→ to see if the equation holds true; i.e. to see if both sides of the equation are equal when: " m = 4 " ;
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We have:
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→ " 3(m − 2) = ? (3*m) − (3*2) " ?? ;
First let us rewrite this equation; substitute "4" for "m" ; as follows:
→ " 3(4 − 2) = ? (3*4) − (3*2) " ?? ;
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And calculate; to see if each side of the equation is equal ; i.e. to see if the equation holds true; as follows:
→ " 3(2) = ? (12) − (6) " ?? ;
→ " 6 = ? (6) " ?? ;
→ " 6 = 6 " ! Yes! The equation holds true!
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Hope this answer was helpful!
Best wishes!
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