Question

Complete the statement to describe the expression (a+b)(d+e)(a+b)(d+e)left parenthesis, a, plus, b, right parenthesis, left parenthesis, d, plus, e, right parenthesis. The expression consists of factors, and each factor contains 4 terms.

Answer 1

Explanation:

Terms are single numbers, variables, or the product of a number and variable.A factor is one part of a product.Hint #22 / 4The expression (a+b+c)(d+e+f)(a+b+c)(d+e+f)start color #df0030, left parenthesis, a, plus, b, plus, c, right parenthesis, end color #df0030, start color #6495ed, left parenthesis, d, plus, e, plus, f, right parenthesis, end color #6495ed consists of two things multiplied together, so we say the expression has two factors. The first factor is (a+b+c)(a+b+c)start color #df0030, left parenthesis, a, plus, b, plus, c, right parenthesis, end color #df0030 and the second is (d+e+f)(d+e+f)start color #6495ed, left parenthesis, d, plus, e, plus, f, right parenthesis, end color #6495ed.Hint #33 / 4Each of the factors contains the sum of three variables. Variables connected by addition are separate terms. The expression (a+b+c)(a+b+c)start color #df0030, left parenthesis, a, plus, b, plus, c, right parenthesis, end color #df0030 contains three terms: aastart color #df0030, a, end color #df0030, bbstart color #df0030, b, end color #df0030, ccstart color #df0030, c, end color #df0030. The expression (d+e+f)(d+e+f)start color #6495ed, left parenthesis, d, plus, e, plus, f, right parenthesis, end color #6495ed also contains three terms.Hint #44 / 4The expression (a+b+c)(d+e+f)(a+b+c)(d+e+f)left parenthesis, a, plus, b, plus, c, right parenthesis, left parenthesis, d, plus, e, plus, f, right parenthesis consists of 222 factors, and each of these factors has 333terms.

Answer 2

The expression contains two factor and each factor contains 2 terms.

Explanation:

We are given the expression:

`(a+b)(d+e)(a+b)(d+e) = (a+b)^2(d+e)^2`

• A factor can be a number, variable, term, or a longer expression.
• A factor is made of of terms and can be a constant, number or a variable.

Now, the expression contains two factor and each factor contains 2 terms.

The factors of expression are:

`1. ~(a+b)\\\text{This factor have a multiplicity of 2 in the expression.}\\2.~ (d+e)\\\text{This factor have a multiplicity of 2 in the expression.}`

The terms of expression are:

`1.~(a+b) \text{ have terms a and b}\\2.~(d+e) \text{ have terms d and e}`