Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. which statements are true about the process and simplified product? check all that apply.
1. the term –2(x – 2)2 is simplified by first squaring the expression x – 2.
2. the simplified product is a binomial.
3. after multiplying, the like terms are combined by adding and subtracting.
4. the parentheses are eliminated through multiplication.
5. the final simplified product is –28x2 +8x – 8.

1,3,4

Step-by-step explanation:

Given expression

3x(x-12x)+3x^2-2(x-2)^2

To solve the expression the whole square if x-2 will be evaluated first:

=3x(x-12x)+3x^2-2(x^2-4x+4)

Then, solving the brackets:

=3x(-11x)+3x^2-2x^2+8x-8

= -33x^2+3x^2-  2x^2+8x-8

= -32x^2+8x-8

Now lets look at the options one by one:

1. The term –2(x – 2)2 is simplified by first squaring the expression x – 2.

Statement 1 is true as the square will be solved first.

2. The simplified product is a binomial.

Statement 2 is false as the resulting expression is trinomial.

3. After multiplying, the like terms are combined by adding and subtracting.

Statement 3 is correct as the like terms with same variables are added.

4. The parentheses are eliminated through multiplication.

Statement 4 is correct. The brackets are solved by multiplying the integers into the brackets.

5. The final simplified product is –28x2 +8x – 8.

Statement 5 is false as the result is = -32x^2+8x-8  ..

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98