We are given expression: [tex]3a^3x(4a^2bcx^3)[/tex]
3a^3x is in front of Parenthesis.
So, we need to apply multiplication operation there.
We need to multiply like terms( numbers by number and variables by variables).
First we multiply 3 * 4, it gives 12.
Now, a^3 * a^2. In order to multiply a^3 * a^2, we need to apply product rule of exponents.
According to product rule of exponents, when bases are same, we just need to add the exponents by keeping same base.
Therefore, [tex]a^3*a^2=a^{3+2}[/tex]=[tex]x^5[/tex]
On the same way, we can apply apply product rule of exponents on multiplication of
x and x^3.
[tex]x * x^3 = x^{1+3} = x^4.[/tex]
Therefore, final answer would be
[tex]3a^3x(4a^2bcx^3)=12a^5bx^4[/tex].
Answer:
When you multiply you add exponents on like terms and multiply coefficients. The 3 is the coefficient of a^3x and 4 is the coefficient of a^2bcx^3. The a's are like terms and x's are like terms. There is only one use of b and c. So, multiplying coefficients -- 3*4 =12. Multiplying a^3 times a^2 equals a^5, and x times x^3 equals x^4. Answer is 12a^5bcx^4.
