To factorize the expression completely:
[tex]\[ 21a^2 + 28ab \][/tex]
we will follow these steps:
1. Identify the common factors for the terms:
- The first term is [tex]\(21a^2\)[/tex]. The factors of [tex]\(21a^2\)[/tex] are [tex]\(21\)[/tex] and [tex]\(a^2\)[/tex], which can be further factored to [tex]\(3 \times 7 \times a \times a\)[/tex].
- The second term is [tex]\(28ab\)[/tex]. The factors of [tex]\(28ab\)[/tex] are [tex]\(28\)[/tex] and [tex]\(ab\)[/tex], which can be further factored to [tex]\(4 \times 7 \times a \times b\)[/tex].
2. Find the greatest common factor (GCF):
- Both terms have a common factor [tex]\(7a\)[/tex].
- Thus, the GCF of [tex]\(21a^2\)[/tex] and [tex]\(28ab\)[/tex] is [tex]\(7a\)[/tex].
3. Factor out the greatest common factor:
- Divide each term by the GCF [tex]\(7a\)[/tex]:
[tex]\[
21a^2 \div 7a = 3a
\][/tex]
[tex]\[
28ab \div 7a = 4b
\][/tex]
4. Write the expression as a product of the GCF and the simplified terms:
- After factoring out [tex]\(7a\)[/tex], the expression becomes:
[tex]\[
21a^2 + 28ab = 7a(3a + 4b)
\][/tex]
So, the completely factorized form of the given expression [tex]\(21a^2 + 28ab\)[/tex] is:
[tex]\[ 7a(3a + 4b) \][/tex]
