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Expanding the Expression: (2x-3)(3x+5)
This article will guide you through expanding the expression (2x-3)(3x+5) using the FOIL method.
Understanding FOIL
FOIL stands for First, Outer, Inner, Last. It's a mnemonic device used to remember the steps involved in multiplying two binomials.
Step 1: First Multiply the first terms of each binomial: (2x) * (3x) = 6x²
Step 2: Outer Multiply the outer terms of each binomial: (2x) * (5) = 10x
Step 3: Inner Multiply the inner terms of each binomial: (-3) * (3x) = -9x
Step 4: Last Multiply the last terms of each binomial: (-3) * (5) = -15
Combining Like Terms
Now we have: 6x² + 10x - 9x - 15
Combine the like terms (the terms with 'x'): 6x² + x - 15
The Final Answer
Therefore, the expanded form of (2x-3)(3x+5) is 6x² + x - 15.
Practice Makes Perfect
Remember, practicing with different binomial expressions will help you master the FOIL method.
For example: Try expanding (x+2)(x-4). You can always check your answer by using online calculators or by working through the steps yourself.