Introduction to Factoring a Linear Expression via the Distributive Property
Introduction to Factoring a Linear Expression via the Distributive Property is a Grade 7 math skill from Big Ideas Math, Course 2, covering Expressions and Equations. Factoring a linear expression involves rewriting it as a product of its factors. This is done by finding the greatest common factor (GCF) of the terms and applying the distributive property in reverse: Here, is the GCF of the terms and . Explanation Factoring is the process of rewriting an expression as a product of its factors, which is the reverse of distribution.
Key Concepts
Property Factoring a linear expression involves rewriting it as a product of its factors. This is done by finding the greatest common factor (GCF) of the terms and applying the distributive property in reverse: $$ab + ac = a(b+c)$$ Here, $a$ is the GCF of the terms $ab$ and $ac$.
Examples Factor $12x + 18$: The GCF of $12$ and $18$ is $6$. So, $12x + 18 = 6(2x) + 6(3) = 6(2x + 3)$. Factor $4y 20$: The GCF of $4$ and $20$ is $4$. So, $4y 20 = 4(y) 4(5) = 4(y 5)$. Factor $\frac{1}{2}x + \frac{3}{2}$: The GCF of $\frac{1}{2}$ and $\frac{3}{2}$ is $\frac{1}{2}$. So, $\frac{1}{2}x + \frac{3}{2} = \frac{1}{2}(x) + \frac{1}{2}(3) = \frac{1}{2}(x + 3)$.
Explanation Factoring is the process of rewriting an expression as a product of its factors, which is the reverse of distribution. To factor a linear expression, first identify the greatest common factor (GCF) of the numerical coefficients and constants. Then, divide each term in the expression by the GCF to determine the remaining factor inside the parentheses. This method can be applied to expressions with integer or fractional coefficients.
Common Questions
What is introduction to factoring a linear expression via the distributive property?
Factoring a linear expression involves rewriting it as a product of its factors.. This is done by finding the greatest common factor (GCF) of the terms and applying the distributive property in reverse: Here, is the GCF of the terms and .
How do you use introduction to factoring a linear expression via the distributive property in Grade 7?
Explanation Factoring is the process of rewriting an expression as a product of its factors, which is the reverse of distribution.. To factor a linear expression, first identify the greatest common factor (GCF) of the numerical coefficients and constants.. Then, divide each term in the expression by the GCF to determine the remaining factor inside the parentheses.
What is an example of introduction to factoring a linear expression via the distributive property?
Examples Factor : The GCF of and is .. Factor : The GCF of and is .. * Factor : The GCF of and is .
Why do Grade 7 students learn introduction to factoring a linear expression via the distributive property?
Mastering introduction to factoring a linear expression via the distributive property helps students build mathematical reasoning. To factor a linear expression, first identify the greatest common factor (GCF) of the numerical coefficients and constants.. Then, divide each term in the expression by the GCF to determine the remaining factor inside the parentheses.
What are common mistakes when working with introduction to factoring a linear expression via the distributive property?
A common mistake is overlooking key conditions. Factoring a linear expression involves rewriting it as a product of its factors. This is done by finding the greatest common factor (GCF) of the terms and applying the distributive property in reverse
Where is introduction to factoring a linear expression via the distributive property taught in Big Ideas Math, Course 2?
Big Ideas Math, Course 2 introduces introduction to factoring a linear expression via the distributive property in Expressions and Equations. This skill appears in Grade 7 and connects to related topics in the same chapter.