Question

Factorise: (3x-4y)^4-x^4​

Answer 1

Step-by-step explanation:

lUse the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0n⁡nCk⋅(an-kbk).

4∑k=04!(4−k)!k!⋅(3x)4−k⋅(−4y)k∑k=04⁡4!(4-k)!k!⋅(3x)4-k⋅(-4y)k

Expand the summation.

4!(4−0)!0!⋅(3x)4−0⋅(−4y)0+4!(4−1)!1!⋅(3x)4−1⋅(−4y)+4!(4−2)!2!⋅(3x)4−2⋅(−4y)2+4!(4−3)!3!⋅(3x)4−3⋅(−4y)3+4!(4−4)!4!⋅(3x)4−4⋅(−4y)44!(4-0)!0!⋅(3x)4-0⋅(-4y)0+4!(4-1)!1!⋅(3x)4-1⋅(-4y)+4!(4-2)!2!⋅(3x)4-2⋅(-4y)2+4!(4-3)!3!⋅(3x)4-3⋅(-4y)3+4!(4-4)!4!⋅(3x)4-4⋅(-4y)4

Simplify the exponents for each term of the expansion.

1⋅(3x)4⋅(−4y)0+4⋅(3x)3⋅(

Answer 2

Step-by-step explanation:

I hope it helps you...

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