Can you check my answer and the work? Thank youu~~
(2x-y)7
128x7 -448x6y -672x5y2 -560x4y3 -280x3y4 -84x2y5 -14xy6 -y7
orr
128x7 -448x6y +672x5y2 - 560x4y3 +280x3y4 -84x2y5 +14xy6 -y7
Ps: the 7 in the equation is the exponent and the numbers after the variable are also the exponent
+ 672x^5y^2 - 280x^3y^4 + 14xy^6
only the signs were wrong for the above
corrections
I used an online calculator to expand so I know it's right
so is it this?
128x7 -448x6y +672x5y2 - 560x4y3 +280x3y4 -84x2y5 +14xy6 -y7
or
128x7 -448x6y +672x5y2 -280x3y4 +14xy6
?
sorry, I didn't see your 2nd line after
"or", so the correction applies to your first line/answer
k thank youuu~~~ =)
you're welcome
To verify your answer, we can expand the expression using the binomial expansion formula.
The binomial expansion formula is given as:
(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n
In this case, the expression is (2x-y)^7.
We can rewrite this as:
(2x - y)^7 = C70 * (2x)^7 * (-y)^0 + C71 * (2x)^6 * (-y)^1 + C72 * (2x)^5 * (-y)^2 + ... + C77 * (2x)^0 * (-y)^7
Where Cnr represents the binomial coefficient, defined as n! / (r! * (n-r)!).
Now, let's simplify it step by step.
C70 * (2x)^7 * (-y)^0 simplifies to:
1 * (2x)^7 * 1 = 128x^7
Next, C71 * (2x)^6 * (-y)^1 simplifies to:
7 * (2x)^6 * (-y) = -448x^6y
Continuing this process for each term, we get the following expression:
128x^7 - 448x^6y + 672x^5y^2 - 560x^4y^3 + 280x^3y^4 - 84x^2y^5 + 14xy^6 - y^7
Comparing this with your answer, it matches the second expression you provided:
128x^7 - 448x^6y + 672x^5y^2 - 560x^4y^3 + 280x^3y^4 - 84x^2y^5 + 14xy^6 - y^7
Therefore, your second answer is correct.