Question

(5c+7d)^2-70cd= (8m-n)^2-64m= (3a-b)(3a+b)+b^2= 9x^2-(y+4x)(y-4x)= (5c-6d)(5c+6d)-25c^2= (7m-10n)(7m+10n)-100^2= 2(a-2)(a+2)= x(x+4)(x-4)= 5c(c+3)(c-3)= 7d^2(d-1)(d+1)=

Answer 1

(5c+7d)^2-70cd=25c^2+70cd+49d^2-70cd=25c^2+49d^2(8m-n)^2-64m=64m^2-16mn+n^2-64m=64m^2-80mn+n^2
(3a-b)(3a+b)+b^2=9a^2-b^2+b^2=9a^2
9x^2-(y+4x)(y-4x)=9x^2-y^2+16x^2=25x^2-y^2
(5c-6d)(5c+6d)-25c^2=25c^2-36d^2-25c^2=-36d^2
(7m-10n)(7m+10n)-100n^2=49m^2-100n^2-100n^2=49m^2-200n^2
2(a-2)(a+2)=9(a^2-4)=9a^2-36
x(x+4)(x-4)=x(x^2-16)=x^3-16x
5c(c+3)(c-3)=5c(c^2-9)=5c^3-45c
7d^2(d-1)(d+1)=7d^2(d^2-1)=7d^4-7d^2
если есть ошибки без обид

Answer 2

Let's simplify each of the given expressions:

1. $(5c+7d)^2-70cd$: Expand the square: $(5c+7d)^2 = 25c^2 + 70cd + 49d^2$ Now subtract $70cd$: $(25c^2 + 70cd + 49d^2) - 70cd = 25c^2 + 49d^2$

2. $(8m-n)^2-64m$: Expand the square: $(8m-n)^2 = 64m^2 - 16mn + n^2$ Now subtract $64m$: $(64m^2 - 16mn + n^2) - 64m = 64m^2 - 16mn + n^2 - 64m$

3. $(3a-b)(3a+b)+b^2$: Use the difference of squares formula: $a^2 - b^2 = (a+b)(a-b)$ Applying this to your expression: $(3a-b)(3a+b) = (3a)^2 - b^2 = 9a^2 - b^2$ Now add $b^2$: $9a^2 - b^2 + b^2 = 9a^2$

4. $9x^2-(y+4x)(y-4x)$: This is another difference of squares: $(y+4x)(y-4x) = y^2 - (4x)^2 = y^2 - 16x^2$ Now subtract this from $9x^2$: $9x^2 - (y^2 - 16x^2) = 9x^2 - y^2 + 16x^2$

5. $(5c-6d)(5c+6d)-25c^2$: Again, this is a difference of squares: $(5c-6d)(5c+6d) = (5c)^2 - (6d)^2 = 25c^2 - 36d^2$ Now subtract $25c^2$: $25c^2 - 36d^2 - 25c^2 = -36d^2$

6. $(7m-10n)(7m+10n)-100^2$: Once more, this is a difference of squares: $(7m-10n)(7m+10n) = (7m)^2 - (10n)^2 = 49m^2 - 100n^2$ Now subtract $100^2$: $49m^2 - 100n^2 - 100^2 = 49m^2 - 10000n^2$