Question

X2-4y2 (a+3b)2(2m-5n)2(8x+3y)2(7c-4a)2(10d-2m)2Если что Двойка это квадрат

Answer 1

=(x-4y)(x+4y)

=a2 + 9b2 +6ab

=4m2 +25n2 - 20mn

=64x2 + 9y2 + 48xy

=49c2 + 16a2 - 56ca

=100d2 + 4m2 - 40dm

Answer 2

It seems like you want to simplify the expression $X^2-4y^2\cdot (a+3b)^2\cdot(2m-5n)^2\cdot(8x+3y)^2\cdot(7c-4a)^2\cdot(10d-2m)^2$. To do this, we'll start by using some basic rules of algebra and expanding the given expression.

Step 1: Apply the square of a binomial formula for $a+3b$, $2m-5n$, $8x+3y$, $7c-4a$, and $10d-2m$.

$(a+3b)^2 = a^2 + 2ab + 3b^2$

$(2m-5n)^2 = (2m)^2 - 2\cdot 2m\cdot 5n + (5n)^2 = 4m^2 - 20mn + 25n^2$

$(8x+3y)^2 = (8x)^2 + 2\cdot 8x\cdot 3y + (3y)^2 = 64x^2 + 48xy + 9y^2$

$(7c-4a)^2 = (7c)^2 - 2\cdot 7c\cdot 4a + (4a)^2 = 49c^2 - 56ac + 16a^2$

$(10d-2m)^2 = (10d)^2 - 2\cdot 10d\cdot 2m + (2m)^2 = 100d^2 - 40dm + 4m^2$

Step 2: Substitute the expanded expressions back into the original expression.

$X^2-4y^2\cdot (a+3b)^2\cdot(2m-5n)^2\cdot(8x+3y)^2\cdot(7c-4a)^2\cdot(10d-2m)^2$

$= X^2 - 4y^2\cdot (a^2 + 2ab + 3b^2)\cdot (4m^2 - 20mn + 25n^2)\cdot (64x^2 + 48xy + 9y^2)\cdot (49c^2 - 56ac + 16a^2)\cdot (100d^2 - 40dm + 4m^2)$

Step 3: Expand further and combine like terms.

Now, multiply the terms together using the distributive property:

$= X^2 - 4y^2\cdot(4m^2 - 20mn + 25n^2)\cdot(64x^2 + 48xy + 9y^2)\cdot(49c^2 - 56ac + 16a^2)\cdot(100d^2 - 40dm + 4m^2)$