Answer: The correct answer is: " 2x² " .
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Step-by-step explanation:
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We are asked: "What is the sum of: "x + x² + 2" and "x² − 2 − x" ?
Since we are to find the "sum" ;
→ We are to "add" these 2 (two) expressions together:
→ (x + x² + 2) + (x² − 2 − x) ;
Note: Let us rewrite the above, by adding the number "1" as a coefficient to: the values "x" ; and "x² " ; since there is an "implied coefficient of "1" ;
→ {since: "any value" ; multiplied by "1"; results in that exact same value.}.
→ (1x + 1x² + 2) + (1x² − 2 − 1x) ;
Rewrite as:
→ 1x + 1x² + 2) + (1x² − 2 − 1x) ;
Now, let us add the "coefficient" , "1" ; just before the expression:
"(1x² − 2 − 1x)" ;
{since "any value", multiplied by "1" , equals that same value.}.
And rewrite the expression; as follows:
→ (1x + 1x² + 2) + 1(1x² − 2 − 1x) ;
Now, let us consider the following part of the expression:
→ " +1(1x² − 2 − 1x) " ;
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Note the distributive property of multiplication:
→ " a(b+c) = ab + ac " ;
and likewise:
→ " a(b+c+d) = ab + ac + ad " .
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So; we have:
→ " +1(1x² − 2 − 1x) " ;
= (+1 * 1x²) + (+1 *-2) + (+1*-1x) ;
= + 1x² + (-2) + (-1x) ;
= +1x² − 2 − 1x ;
↔ ( + 1x² − 1x − 2)
Now, bring down the "left-hand side of the expression:
1x + 1x² + 2 ;
and add the rest of the expression:
→ 1x + 1x² + 2 + 1x² − 1x − 2 ;
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Now, simplify by combining the "like terms" ; as follows:
+1x² + 1x² = 2x² ;
+1x − 1x = 0 ;
+ 2 − 2 = 0 ;
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The answer is: " 2x² " .
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Hope this is helpful to you!
Best wishes!
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