To solve the expression [tex]\( 49x^2 + 42x + 9y^2 \)[/tex], we can approach it step-by-step to understand the different components of the expression.
1. Identify Each Term:
- The given expression is [tex]\( 49x^2 + 42x + 9y^2 \)[/tex].
- This expression is a polynomial with three distinct terms.
2. Analyze Each Term:
- The first term is [tex]\( 49x^2 \)[/tex]. This term is a quadratic term in [tex]\( x \)[/tex] because it involves [tex]\( x \)[/tex] raised to the power of 2 and multiplied by the coefficient 49.
- The second term is [tex]\( 42x \)[/tex]. This term is a linear term in [tex]\( x \)[/tex] because it involves [tex]\( x \)[/tex] raised to the power of 1 and multiplied by the coefficient 42.
- The third term is [tex]\( 9y^2 \)[/tex]. This term is a quadratic term in [tex]\( y \)[/tex] because it involves [tex]\( y \)[/tex] raised to the power of 2 and multiplied by the coefficient 9.
3. Combine the Terms:
- Together, these terms form the polynomial [tex]\( 49x^2 + 42x + 9y^2 \)[/tex], which cannot be simplified further because the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are not combined and the terms are already in their simplest form.
4. Understanding the Expression:
- The expression [tex]\( 49x^2 + 42x + 9y^2 \)[/tex] represents a combination of quadratic and linear terms in [tex]\( x \)[/tex] and a quadratic term in [tex]\( y \)[/tex]. It incorporates elements of both a quadratic polynomial in [tex]\( x \)[/tex] and a quadratic influence from [tex]\( y \)[/tex], making it a multivariable polynomial.
Therefore, the final simplified form and the expression in its most compact form is:
[tex]\[ 49x^2 + 42x + 9y^2 \][/tex]
This is already the simplest and most accurate representation of the given polynomial expression.
