Four equivalent expressions for B plus A are:
These expressions represent the same mathematical operation, simply rearranged or represented differently.
4a + 4b is one possible answer.
To determine if (8a - 3b - (2a - 4b)) is equivalent to (6a + b), we first simplify the left expression. Distributing the negative sign gives us (8a - 3b - 2a + 4b), which simplifies to (6a + b). Since both expressions equal (6a + b), they are indeed equivalent.
(b + 4)(b + 4)
You can use properties such as the distributive property, associative property, and commutative property to write equivalent expressions. For example, the distributive property allows you to expand or factor expressions, like rewriting (a(b + c)) as (ab + ac). The commutative property enables you to change the order of terms, such as (a + b) becoming (b + a), while the associative property lets you regroup terms, such as ((a + b) + c) being rewritten as (a + (b + c)). By applying these properties, you can create different but equivalent forms of the same expression.
3b+4 = b+12 3b-b = 12-4 2b = 8 b = 4
4b-b
4a + 4b is one possible answer.
It is 6*(b + 4)
(b + 4)(b + 4)
A plus b 4 can be assumed that mathematically, a = +4.
7
You can use properties such as the distributive property, associative property, and commutative property to write equivalent expressions. For example, the distributive property allows you to expand or factor expressions, like rewriting (a(b + c)) as (ab + ac). The commutative property enables you to change the order of terms, such as (a + b) becoming (b + a), while the associative property lets you regroup terms, such as ((a + b) + c) being rewritten as (a + (b + c)). By applying these properties, you can create different but equivalent forms of the same expression.
If the rational expressions have large exponent, then you need to factor out this way: (a + b)ⁿ = (a + b)(a + b)...(a + b) [So there are n "(a + b)" factors.] Here are the examples... (a + b)³ = (a + b)(a + b)(a + b) (a + b)4 = (a + b)(a + b)(a + b)(a + b)
The difference ( a - b ) can be restated as an equivalent addition statement by rewriting it as ( a + (-b) ). This shows that subtracting ( b ) from ( a ) is the same as adding the negative of ( b ) to ( a ). Thus, both expressions yield the same result.
3b+4 = b+12 3b-b = 12-4 2b = 8 b = 4
(b+h)(b+h)= b2+2hb+h2.
You must have seen expressions such as 3:4::12:16, which reads 3 is to 4 as 12 is to 16. Sometimes encountered as 5:a::30:b, which is read 5 is to a as 30 is to b. Is this the type of ratio to which you refer.