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Zorluk: KolaySimplifying Algebraic Expressions

An engineer is calculating the total weight supported by two structural pillars. The weight on the first pillar is given by the algebraic expression 5y−25y - 2, and the weight on the second pillar is given by 3y+63y + 6. What is the fully simplified algebraic expression for the total weight supported by both pillars combined?

Cevap: 8y + 4 / 8y+4 / 4 + 8y / 4+8y / 8y +4 / 8y+ 4 / 8y+ 4

Cevap

8y + 4
The total weight is found by adding the two individual weight expressions. By identifying and grouping like terms, the variable terms are combined (5y+3y=8y5y + 3y = 8y) and the constant terms are combined (−2+6=4-2 + 6 = 4) to get the final simplified expression of 8y+48y + 4.

Adım Adım Çözüm

1
Set up the addition of the two individual expressions
(5y−2)+(3y+6)(5y - 2) + (3y + 6)
To find the total weight, both individual weight expressions must be added together.
2
Group the like terms
(5y+3y)+(−2+6)(5y + 3y) + (-2 + 6)
Like terms (terms with the same variable, and constant terms) must be grouped to simplify the expression.
3
Combine the grouped terms
8y+48y + 4
Adding the coefficients of yy (5+3=85 + 3 = 8) and adding the constants (−2+6=4-2 + 6 = 4) yields the fully simplified form.

Anahtar Kavram

Combining Like Terms
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Konular

Simplifying Algebraic Expressions

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