Complete the Expression with Distributive Property: x(x + 5) = ? + 5x - Math Solver AI

$Math Problem$

Mathematics Grade 7

Question Content

Use the distributive property to complete the statement: x(x + 5) = ____ + 5x

Correct Answer

x²

Detailed Solution Steps

1
Step 1: Recall the distributive property: c(a+b) = ca + cb.
2
Step 2: Apply the property to x(x+5): multiply x by each term inside the parentheses. x×x = x², x×5 = 5x.
3
Step 3: Fill in the blank with x².

Knowledge Points Involved

1

Distributive Property with Variable Multipliers

The distributive property applies to variables as well as constants: x(a+b) = xa + xb. When multiplying a variable by itself, x×x = x², following the rule of exponents for like bases.

2

Exponent Rule for Multiplying Like Bases

When multiplying two terms with the same base, add the exponents: x^m × x^n = x^(m+n). For x×x, m=1, n=1, so x×x = x^(1+1) = x².

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