i need help with this quretsion ; i don't know if im right, and i dontknwo what do next
question expand and simplfy:
4√7(2√3 + 3√6 - √7)
my work
= 8√21 + 12√42 -4√49
please help me
Yes, but the sqrt49 is widely known as 7
4�ã7(2�ã3+3�ã6- �ã7)
=4*2*�ã7*�ã3 +4*3*�ã7*�ã6 -4*�ã7*�ã7
=8*�ã21 +12*�ã42 -4*�ã49
=8*�ã21+ 12*�ã(21*2) -4*7
=8*�ã21 +12*�ã21+ 12*�ã2- 28
=4*2*�ã21 +4*3*�ã21 +4*3*�ã2 -28
=4*�ã21*(2+3*�ã2)-28
To expand and simplify the given expression 4√7(2√3 + 3√6 - √7), you can follow these steps:
Step 1: Multiply 4√7 by each term inside the parentheses.
Step 2: Simplify each resulting term by applying the rules of square roots.
Step 3: Combine like terms, if any.
Let's work through it step by step:
Step 1: Multiply 4√7 by each term inside the parentheses:
4√7 * 2√3 = 8√21
4√7 * 3√6 = 12√42
4√7 * -√7 = -28
So, the expression becomes: 8√21 + 12√42 -28
Step 2: Simplify each resulting term:
8√21 cannot be simplified further because 21 does not have any perfect square factors.
12√42 can be simplified by recognizing that 42 can be factored into 2 * 21, so:
12√42 = 12√(2 * 21) = 12√2√21 = 12√2 * √21 = 12√2√7
So, the expression now becomes: 8√21 + 12√2√7 - 28
Step 3: Combine like terms, if any.
Since there are no like terms in this expression, we can consider it simplified.
Therefore, the final simplified form of the expression 4√7(2√3 + 3√6 - √7) is:
8√21 + 12√2√7 - 28.