i need help with simplying algerbraic expression
1) m^2 p^2 + mpg - 6g^2 =
2) 2h^3 + 2h^2t - 4ht^2
1. m^2p^2 + mpg - 6g^2
(mp + 3g) (mp - 2g).
2. 2h^3 + 2h^2t - 4ht^2
Factor using A*C Method:
A * C =2 * -4 = -8
2h^3 - 2h^2t+4h^2t - 4ht^2=
Group the 4 terms in factorable pairs
and factor:
(2h^3 - 2h^2t) + (4h^2t - 4ht^2),
2h^2(h - t) + 4ht(h - t),
Factor out (h - t):
(h - t) (2h^2 +4ht),
Factor the binomial:
(h - t) (2h) (h + 2t).
what property is described by this equation? 24×5=(20×5)+(4×5)
To simplify algebraic expressions, you need to combine like terms and simplify as much as possible. Let's work through the two expressions you provided:
1) m^2 p^2 + mpg - 6g^2:
To simplify this expression, look for terms that have the same variables and exponents. In this case, we have three terms: m^2 p^2, mpg, and -6g^2. None of these terms have the same variables and exponents, so we cannot combine them.
Therefore, the expression remains as m^2 p^2 + mpg - 6g^2.
2) 2h^3 + 2h^2t - 4ht^2:
Similarly, let's look for terms that have the same variables and exponents. In this case, we have three terms: 2h^3, 2h^2t, and -4ht^2. Notice that all three terms have the variable h, but the exponents are different.
We cannot combine the terms as they are, but we can factor out the common variable h. The highest exponent of h is 3, so we can factor out h^2 from each term:
2h^2 (h + t - 2t^2)
Now we have factored out the common term 2h^2, and we are left with the simplified expression of 2h^2 (h + t - 2t^2).
Remember, simplifying algebraic expressions involves combining like terms and factoring out common factors. Keep practicing, and you'll get better at simplifying expressions!