Problem 99 Simplify. $$ 3(1-x y)-2(x y-... [FREE SOLUTION]

Chapter 1: Problem 99

Simplify. $$ 3(1-x y)-2(x y-5)-(35-x y) $$

Short Answer

Expert verified

\[ -22 - 4 x y \]

Step by step solution

- Distribute

Apply the distributive property to each term in the parentheses: \[ 3(1 - x y) = 3 - 3 x y \] \[ -2(x y - 5) = -2 x y + 10 \] \[ -(35 - x y) = -35 + x y \]

- Combine Like Terms

Combine the terms with the same variables and the constant terms: \[ 3 - 3 x y - 2 x y + 10 - 35 + x y \]

- Simplify the Expression

Group and simplify the constants and the terms involving xy: \[ 3 + 10 - 35 + (-3 x y - 2 x y + x y) = -22 - 4 x y \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property

Using the distributive property can sometimes seem tricky, but it's an essential tool in algebra. The basic idea is to multiply each term inside the parentheses by the term outside. For example, in the expression $3(1 - xy)$, you multiply both $1$ and $-xy$ by $3$. So, $3(1 - xy) = 3 - 3xy$.

Let鈥檚 look at all parts of our original problem:

For $-2(xy - 5)$, multiply $-2$ by each term inside: $-2(xy - 5) = -2xy + 10$.
For $-(35 - xy)$, distribute the $-1$: $-(35 - xy) = -35 + xy$.

The result after applying the distributive property is:
\[3 - 3xy - 2xy + 10 - 35 + xy\]
Each term now stands alone, and we can move on to the next step!

Combining Like Terms

Combining like terms means adding or subtracting the coefficients of terms that have the same variable component. This step helps to further simplify the expression. Look at the terms in your expression:
\[3 - 3xy - 2xy + 10 - 35 + xy\]
Separate the constants (numbers without variables) and the variable terms (terms with $xy$):

Constants: $3, 10, -35$
Terms with $xy$: $-3xy, -2xy, xy$

Combine the constants:
$3 + 10 - 35 = -22$
Now combine the variable terms:
$-3xy - 2xy + xy = -4xy$
Once all like terms are combined, you'll have a simplified expression!

Algebraic Simplification

The final step in simplifying our expression is just putting it all together. From combining like terms, we found our constants sum to $-22$ and our variable terms combine to $-4xy$.
When we write it all out, our simplified expression is:
\[-22 - 4xy\]
Simplifying expressions is a process of methodically applying properties like the distributive property and combining like terms.

First, distribute to remove parentheses.
Next, combine like terms by grouping constants and variables.
Finally, simplify as much as possible.

Remember, practice makes perfect with these techniques! Each problem helps reinforce your skills in algebraic simplification.

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91影视

Simplify. $$ 3(1-x y)-2(x y-5)-(35-x y) $$

Short Answer

Step by step solution

- Distribute

- Combine Like Terms

- Simplify the Expression

Key Concepts

Distributive Property

Combining Like Terms

Algebraic Simplification

One App. One Place for Learning.

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