(x%2B10)-using-identities.jpeg "(x+4)(x+10) Using Identities")
Expanding (x+4)(x+10) using Identities
We can expand the expression (x+4)(x+10) using the distributive property or the identity (a+b)(c+d) = ac + ad + bc + bd. Let's explore both methods.
Method 1: Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Applying this to our expression:
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Step 1: Distribute (x+4) over (x+10).
- (x+4)(x+10) = x(x+10) + 4(x+10)
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Step 2: Distribute x and 4 individually.
- x(x+10) + 4(x+10) = x² + 10x + 4x + 40
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Step 3: Combine like terms.
- x² + 10x + 4x + 40 = x² + 14x + 40
Therefore, (x+4)(x+10) expanded using the distributive property is x² + 14x + 40.
Method 2: Identity (a+b)(c+d)
The identity (a+b)(c+d) = ac + ad + bc + bd allows us to directly expand the expression without multiple steps.
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Step 1: Identify a, b, c, and d.
- In our case, a = x, b = 4, c = x, and d = 10.
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Step 2: Substitute the values into the identity.
- (x+4)(x+10) = xx + x10 + 4x + 410
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Step 3: Simplify the expression.
- xx + x10 + 4x + 410 = x² + 14x + 40
Using the identity, we again arrive at the same expanded form: x² + 14x + 40.
Conclusion
Both methods provide the same result for expanding (x+4)(x+10). The choice of method depends on personal preference and the complexity of the expression. The identity method can be quicker for simple expressions while the distributive property might be more intuitive for some individuals.