Alright, let's go through a detailed, step-by-step breakdown of the expression [tex]\( -3x^2 + 7y^3 \)[/tex].
1. Identify the variables:
The expression involves two variables, [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
2. Identify the coefficients:
- The coefficient of [tex]\( x^2 \)[/tex] is [tex]\( -3 \)[/tex]. This means that [tex]\( -3 \)[/tex] is multiplied by the square of [tex]\( x \)[/tex].
- The coefficient of [tex]\( y^3 \)[/tex] is [tex]\( 7 \)[/tex]. This means that [tex]\( 7 \)[/tex] is multiplied by the cube of [tex]\( y \)[/tex].
3. Identify the terms:
The expression consists of two separate terms:
- The first term is [tex]\( -3x^2 \)[/tex].
- The second term is [tex]\( 7y^3 \)[/tex].
4. Understanding the powers:
- [tex]\( x^2 \)[/tex] indicates that [tex]\( x \)[/tex] is raised to the power of 2, which is a quadratic term.
- [tex]\( y^3 \)[/tex] indicates that [tex]\( y \)[/tex] is raised to the power of 3, which is a cubic term.
5. Combining the terms:
The expression is a sum of the two terms:
- The first term [tex]\( -3x^2 \)[/tex] has [tex]\( x \)[/tex] squared and then multiplied by -3.
- The second term [tex]\( 7y^3 \)[/tex] has [tex]\( y \)[/tex] cubed and then multiplied by 7.
In summary, the expression [tex]\( -3x^2 + 7y^3 \)[/tex] consists of a quadratic term in [tex]\( x \)[/tex] with coefficient -3 and a cubic term in [tex]\( y \)[/tex] with coefficient 7.
So, [tex]\( -3x^2 + 7y^3 \)[/tex] is an algebraic expression that represents the sum of two terms: a quadratic term in [tex]\( x \)[/tex] and a cubic term in [tex]\( y \)[/tex].
