To subtract fractions, we need an lcd( lowest common denominator)
8. the lcd is 42 because it’s the smallest number that 6 and 7 are both factors of. the lcd is the bottom of the fraction
to make the denominator of (4/7) 42, we will multiply the top and bottom by 6 and we get (24/42)
to make the denominator of (3/6) 42, we will multiply the top and bottom by 7 and we get (21/42)
these two numbers now have the same denominator so we subtract them
24/42 - 21/42 = 3/42 which simplifies to 1/14
9. since these fractions already have a common denominator, we will make them mixed fractions
-5(2/7) as a mixed fraction. first multiply 5*7 which is 35. now add 2 which is 37. our mixed fraction is -37/7
-1(5/7) as a mixed fraction. multiple 1*7 which is 7. now add 5 which is 12. our mixed fraction is -12/7
now subtract (-37/7) - (12/7) and we get -49/7 which simplifies to -7
(3m+5n)(9m²-15mn+25n²)
1) Let's factorize 27m³ +125n³.
27m³ +125n³ <em>Let's use x³ +y³ product to factorize that</em>
<em />
x³ +y³ = (x +y)(x²-xy +y²)
2) So let's rewrite it, since 3³ = 27 and 5³ = 125
27m³ +125n³ =
Plug x =3m and y = 5n into those factors (x +y)(x²-xy +y²)
27m³ +125n³= (3m + 5n)(3²m² -5n*3m +5²n²)
27m³ +125n³= (3m+5n)(9m² - 15mn +25n²)
3) So the answer is
(3m+5n)(9m²-15mn+25n²)
<em />
The answer is 1.7 there you go.
