To factor the given expression [tex]\(a x^2 + d x^2\)[/tex] using the distributive property, follow these steps:
1. Identify the common factor: Look at both terms in the expression. Both terms, [tex]\(a x^2\)[/tex] and [tex]\(d x^2\)[/tex], contain the common factor [tex]\(x^2\)[/tex].
2. Factor out the common factor: Use the distributive property to factor out the common factor [tex]\(x^2\)[/tex]. This means representing the expression as the product of [tex]\(x^2\)[/tex] and another expression that includes the remaining parts once [tex]\(x^2\)[/tex] is factored out.
[tex]\[
a x^2 + d x^2 = x^2(a + d)
\][/tex]
3. Write the factored form: After factoring out the common term, the expression simplifies to:
[tex]\[
x^2(a + d)
\][/tex]
Thus, the factored form of the expression [tex]\(a x^2 + d x^2\)[/tex] is [tex]\(\mathbf{x^2(a + d)}\)[/tex]. This shows the original expression written as a single product, illustrating one of the primary uses of the distributive property in algebra.
