(2x-7).jpeg "(3x+2)(2x-7)")
Expanding the Expression (3x + 2)(2x - 7)
This article will guide you through the steps of expanding the expression (3x + 2)(2x - 7).
Understanding the Concept
The expression (3x + 2)(2x - 7) represents the product of two binomials. To expand this expression, we will use the distributive property. This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Step-by-Step Expansion
-
Distribute the first term of the first binomial (3x) to both terms of the second binomial:
- (3x)(2x) = 6x²
- (3x)(-7) = -21x
-
Distribute the second term of the first binomial (2) to both terms of the second binomial:
- (2)(2x) = 4x
- (2)(-7) = -14
-
Combine the four terms you obtained:
- 6x² - 21x + 4x - 14
-
Simplify by combining like terms:
- 6x² - 17x - 14
The Expanded Expression
Therefore, the expanded form of (3x + 2)(2x - 7) is 6x² - 17x - 14.
Summary
By applying the distributive property, we have successfully expanded the expression (3x + 2)(2x - 7) to obtain the equivalent expression 6x² - 17x - 14. This process is crucial in various mathematical operations, particularly when solving equations and simplifying expressions.