Question

(8y-x)(6y-x)(6x+4y)+(8y+x)(6y+x)(-6x+4y)(8y-x)(6y-x)(6x+4y)-(8y+x)(6y+x)(-6x+4y)​

Answer 1

1) (48y²-8xy-6xy+x²)(6x+4y)+(48y²+8xy+6xy+x²)(-6x+4y)=(48y²-14xy+x²)(6x+4y)+(48y²+14xy+x²)(-6x+4y)= 288xy²+192y³-84x²y-56xy²+6x³+4x²y-288xy²+192y³-84x²y+56xy²-6x³+4x²y= 384y³-160x²y

2) (48y²-8xy-6xy+x²)(6x+4y)-(48y²+8xy+6xy+x²)(-6x+4y)=(48y²-14xy+x²)(6x+4y)-(48y²+14xy+x²)(-6x+4y)=288xy²+192y³-84x²y-56xy²+6x³+4x²y+288xy²-192y³+84x²y-56xy²+6x³-4x²y= 464xy²+12x³

Answer 2

Let's simplify the given expression step by step:

1. Expand each term within the parentheses: (8y - x)(6y - x)(6x + 4y) = 288xy^2 - 152x^2y - 16x^3 + 24y^3 (8y + x)(6y + x)(-6x + 4y) = -288xy^2 + 152x^2y + 16x^3 - 24y^3

2. Combine the two expressions: (8y - x)(6y - x)(6x + 4y) - (8y + x)(6y + x)(-6x + 4y) = (288xy^2 - 152x^2y - 16x^3 + 24y^3) - (-288xy^2 + 152x^2y + 16x^3 - 24y^3)

3. Simplify the expression by combining like terms: = 288xy^2 - 152x^2y - 16x^3 + 24y^3 + 288xy^2 - 152x^2y - 16x^3 + 24y^3

4. Now, combine the like terms again: = 576xy^2 - 304x^2y - 32x^3 + 48y^3

So the simplified expression is: 576xy^2 - 304x^2y - 32x^3 + 48y^3.