Expand and Simplify: (x+5)(x+4) Using the Distributive Property


To expand the expression (x+5)(x+4), we can use the distributive property

To expand the expression (x+5)(x+4), we can use the distributive property.

(x+5) will multiply each term inside the second parentheses (x+4), resulting in:

x * (x+4) + 5 * (x+4)

Now we need to simplify each term:

First term: x * (x+4)
Applying the distributive property again, we get:
x * x + x * 4 = x^2 + 4x

Second term: 5 * (x+4)
Again, using the distributive property:
5 * x + 5 * 4 = 5x + 20

Combining the simplified terms, we have:

(x+5)(x+4) = x^2 + 4x + 5x + 20

Finally, simplifying further by combining like terms:

(x+5)(x+4) = x^2 + (4x + 5x) + 20
(x+5)(x+4) = x^2 + 9x + 20

Therefore, the expanded form of (x+5)(x+4) is x^2 + 9x + 20.

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