(3x+7)(5x-2)
Try the FOIL method:
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(3x+7)*(5x-2))=5x*3x+5x*7-2*3x-2*7=15x^2+35x-6x-14=15x^2+29x-14
To multiply the expression (3x + 7)(5x - 2), you can use the distributive property. This property states that when you have a term outside parentheses being multiplied by the sum or difference inside the parentheses, you need to multiply the term by each term inside the parentheses and then combine the like terms.
Here's the step-by-step process to solve (3x + 7)(5x - 2):
Step 1: Multiply the first terms:
Multiply 3x from the first parentheses with 5x from the second parentheses.
(3x)(5x) = 15x²
Step 2: Multiply the outer terms:
Multiply 3x from the first parentheses with -2 from the second parentheses.
(3x)(-2) = -6x
Step 3: Multiply the inner terms:
Multiply 7 from the first parentheses with 5x from the second parentheses.
(7)(5x) = 35x
Step 4: Multiply the last terms:
Multiply 7 from the first parentheses with -2 from the second parentheses.
(7)(-2) = -14
Step 5: Combine the like terms and simplify:
Now, add all the terms together:
15x² - 6x + 35x - 14
Combine the like terms (the terms with the same power of x):
15x² - 6x + 35x - 14 = 15x² + (35x - 6x) - 14 = 15x² + 29x - 14
So, the product of (3x + 7)(5x - 2) is 15x² + 29x - 14.