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anemone
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Factor the expression
\(\displaystyle 30(a^2+b^2+c^2+d^2)+68ab-75ac-156ad-61bc-100bd+87cd\)
\(\displaystyle 30(a^2+b^2+c^2+d^2)+68ab-75ac-156ad-61bc-100bd+87cd\)
anemone said:Factor the expression
\(\displaystyle 30(a^2+b^2+c^2+d^2)+68ab-75ac-156ad-61bc-100bd+87cd\)
Factoring in algebraic expressions is the process of breaking down a polynomial into simpler terms. This involves finding the common factors among the terms and factoring them out to make the expression easier to work with.
Factoring is important in algebra because it allows us to simplify complex expressions and solve equations more easily. It also helps us to identify patterns and relationships among terms, which can be useful in solving more advanced problems.
The first step in factoring an algebraic expression is to look for common factors among the terms. Then, use the distributive property to factor out the common factor. Finally, check if the remaining terms can be factored further using methods such as grouping or the difference of squares.
No, not all algebraic expressions can be factored. Some expressions may not have any common factors or may not have any factors that can be factored out using traditional methods. In these cases, we can use other techniques such as the quadratic formula to solve the expression.
Factoring is used in various fields, such as finance, engineering, and physics. In finance, factoring is used to solve equations involving interest rates and compound interest. In engineering, factoring is used to simplify complex equations and make them easier to solve. In physics, factoring is used to analyze and solve equations related to motion and forces.