Respuesta :
To find which of the given expressions are equivalent to [tex]6g-18h[/tex] we will simplify these given expressions one by one.
A)[tex](g-3)\cdot 6[/tex]
By using distributive property we get[tex]6g-18[/tex]
b) [tex]2\cdot (3g-18h)[/tex]
Upon distributing 2 to the given expression we get
[tex]6g-36h[/tex]
c)[tex]3\cdot (2g-6h)[/tex]
Upon distributing 3 we get
[tex]6g-18h[/tex]
d) [tex](-g-3h)(-6)[/tex]
Upon distributing -6 we get
[tex]6g+18h[/tex]
e) [tex]-2\cdot (-3g+9h)[/tex]
Using distributive property we get
[tex]6g-18h[/tex]
Therefore expressions given in option c and e are equivalent to [tex]6g-18h[/tex]
You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.
The given expression is equivalent to
- Option C) [tex]3(2g-6h)[/tex]
- Option E) [tex]-2\times(-3g+9h)[/tex]
What are equivalent expressions?
Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
What is the distributive property of multiplication over addition?
[tex]a(b + c) = a \times b + a \times c[/tex]
(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times x = 2x[/tex])
The given expression is [tex]6g - 18h[/tex]
We know that we can write
[tex]6 = 2 \times 3\\18 = 2 \times 9 = 3 \times 6[/tex]
Thus,
[tex]6g - 18h = 6 \times g - 6 \times 3h = 6(g - 3h) = -6(-g + 3h)\\\\6g - 18h = 2 \times 3g - 2 \times 9h = 2(3g - 9h) = -2(-3g + 9h)\\\\\\6g - 18h = 3 \times 2g - 3 \times 6h = 3(2g - 6h) = -3(-2g + 6h)[/tex]
All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.
Thus,
The given expression is equivalent to
- Option C) [tex]3(2g-6h)[/tex]
- Option E) [tex]-2\times(-3g+9h)[/tex]
Learn more about equivalent expressions here:
https://brainly.com/question/10628562
