To simplify the expression [tex]\( 15w - 6w + 14w^2 \)[/tex], follow these steps:
1. Combine Like Terms:
Identify and combine the terms involving the same degree of [tex]\( w \)[/tex]:
- The terms [tex]\( 15w \)[/tex] and [tex]\( -6w \)[/tex] are both linear terms (involving [tex]\( w \)[/tex] to the power of 1).
- Combine these terms: [tex]\( 15w - 6w = 9w \)[/tex].
2. Rearrange Terms:
Place the terms in standard form (typically descending order of degree):
- The expression now has two terms: [tex]\( 9w \)[/tex] (linear term) and [tex]\( 14w^2 \)[/tex] (quadratic term).
So, the restructured expression is [tex]\( 14w^2 + 9w \)[/tex].
3. Factor the Expression:
If possible, factor out the greatest common factor (GCF). In [tex]\( 14w^2 + 9w \)[/tex], the common factor is [tex]\( w \)[/tex]:
- Factor out [tex]\( w \)[/tex] from both terms: [tex]\( 14w^2 + 9w = w (14w + 9) \)[/tex].
Hence, the simplified expression is:
[tex]\[ w(14w + 9) \][/tex]
