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Expanding (x+7)(x+5)
In mathematics, expanding an expression often involves removing parentheses using the distributive property. This allows us to simplify the expression and make it easier to work with. In this case, we'll be expanding the expression (x+7)(x+5).
Applying the Distributive Property
The distributive property states that a(b+c) = ab + ac. We can apply this to our expression by treating (x+7) as 'a' and (x+5) as (b+c).
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Distribute the first term of the first parenthesis:
- x * (x+5) = x² + 5x
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Distribute the second term of the first parenthesis:
- 7 * (x+5) = 7x + 35
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Combine the results:
- (x² + 5x) + (7x + 35) = x² + 12x + 35
The Expanded Expression
Therefore, the expanded form of (x+7)(x+5) is x² + 12x + 35.
Understanding the Result
- The x² term is obtained by multiplying the 'x' terms from both parentheses.
- The 12x term is obtained by adding the product of the 'x' term from the first parenthesis and the constant term from the second parenthesis (5x) with the product of the constant term from the first parenthesis and the 'x' term from the second parenthesis (7x).
- The 35 term is obtained by multiplying the constant terms from both parentheses.
By understanding the process of expanding expressions, we gain valuable insights into the relationship between different forms of algebraic expressions and their corresponding simplified forms.