Question

1)6a^2+12ab+6b^2=?2)4x^3-4y^3=?3)-2c^3+128=?4)5ax-5ay+5bx-5by=?5)10a+10y+2pa+2py=?​

Answer 1

Объяснение:

1)6a²+12ab+6b²=

=6(a²+2ab+b²)=

=6(а+b)²  квадрат суммы

2)4x³-4y³=

=4(x³-y³)=  разность кубов

=4(х-у)(х²+ху+у²)

3)-2c³+128=

= -2(c³-64)=   разность кубов  (c³-4³)

= -2(c-4)(c²+4c+16)

4)5ax-5ay+5bx-5by=

=(5ax-5ay)+(5bx-5by)=

=5a(x-y)+5b(x-y)=

=(x-y)(5a+5b)=

=(x-y)5(a+b)=

=5(x-y)(a+b)

5)10a+10y+2pa+2py=

=(10a+2pa)+(10y+2py)=

=2a(5+p)+2y(5+p)=

=(5+p)(2a+2y)=

=(5+p)2(a+y)=

=2(5+p)(a+y)

Answer 2

Let's simplify each expression:

1. 6a^2 + 12ab + 6b^2: To simplify, we can factor out the common terms: 6a^2 + 12ab + 6b^2 = 6(a^2 + 2ab + b^2) Now, we recognize that a^2 + 2ab + b^2 is a perfect square trinomial and can be factored further: 6(a^2 + 2ab + b^2) = 6(a + b)^2

2. 4x^3 - 4y^3: This is a difference of cubes, which can be factored using the formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2) 4x^3 - 4y^3 = 4(x^3 - y^3) Now, we can apply the difference of cubes formula: 4(x^3 - y^3) = 4(x - y)(x^2 + xy + y^2)

3. -2c^3 + 128: This is a simple subtraction: -2c^3 + 128 = 128 - 2c^3

4. 5ax - 5ay + 5bx - 5by: We can factor out 5 from each term: 5ax - 5ay + 5bx - 5by = 5(ax - ay + bx - by) Now, we can rearrange the terms: 5(ax - ay + bx - by) = 5(ax + bx - ay - by) Combine like terms: 5(ax + bx - ay - by) = 5x(a + b) - 5y(a + b) Factor out the common term (a + b): 5x(a + b) - 5y(a + b) = 5(a + b)(x - y)

5. 10a + 10y + 2pa + 2py: Again, we can factor out the common terms: 10a + 10y + 2pa + 2py = 10(a + y) + 2p(a + y) Now, we can factor out (a + y): 10(a + y) + 2p(a + y) = (10 + 2p)(a + y)

So, the simplified expressions are:

1. 6a^2 + 12ab + 6b^2 = 6(a + b)^2
2. 4x^3 - 4y^3 = 4(x - y)(x^2 + xy + y^2)
3. -2c^3 + 128 = 128 - 2c^3
4. 5ax - 5ay + 5bx - 5by = 5(a + b)(x - y)
5. 10a + 10y + 2pa + 2py = (10 + 2p)(a + y)