Answer :
To solve the problem, we need to multiply two expressions: [tex]\( (6x^2) \)[/tex] and [tex]\( (-3x^5) \)[/tex].
Here are the steps to solve the multiplication:
1. Multiply the coefficients:
- Look at the numerical parts first. We have 6 from the first expression and -3 from the second expression.
- Multiply these two numbers: [tex]\( 6 \times (-3) = -18 \)[/tex].
2. Add the exponents of the variable [tex]\( x \)[/tex]:
- In the term [tex]\( 6x^2 \)[/tex], the exponent of [tex]\( x \)[/tex] is 2.
- In the term [tex]\( -3x^5 \)[/tex], the exponent of [tex]\( x \)[/tex] is 5.
- Add these exponents: [tex]\( 2 + 5 = 7 \)[/tex].
3. Combine the results:
- The product of the coefficients gives us the number: -18.
- The sum of the exponents gives us the new exponent of [tex]\( x \)[/tex]: [tex]\( x^7 \)[/tex].
So, the final result of multiplying the two expressions is:
[tex]\[ -18x^7 \][/tex]
Here are the steps to solve the multiplication:
1. Multiply the coefficients:
- Look at the numerical parts first. We have 6 from the first expression and -3 from the second expression.
- Multiply these two numbers: [tex]\( 6 \times (-3) = -18 \)[/tex].
2. Add the exponents of the variable [tex]\( x \)[/tex]:
- In the term [tex]\( 6x^2 \)[/tex], the exponent of [tex]\( x \)[/tex] is 2.
- In the term [tex]\( -3x^5 \)[/tex], the exponent of [tex]\( x \)[/tex] is 5.
- Add these exponents: [tex]\( 2 + 5 = 7 \)[/tex].
3. Combine the results:
- The product of the coefficients gives us the number: -18.
- The sum of the exponents gives us the new exponent of [tex]\( x \)[/tex]: [tex]\( x^7 \)[/tex].
So, the final result of multiplying the two expressions is:
[tex]\[ -18x^7 \][/tex]
