Question

Question 1 (1 point)

Subtract and simplify.

(y2−3y−5)−(−y2−7y+4)
Question 1 options:

2y2+4y−9

2y2−10y+4

−2y2−10y−1
Question 2 (1 point)
Multiply and simplify.

6xy3z⋅3x2yx2
Question 2 options:

18x4y3z

18x5y4z

18(xyz)10
Question 3 (1 point)
Simplify.

−3x3(−2x2+4x−3)
Question 3 options:

−6x6−12x4+9x3

−5x5+x4−6x3

6x5−12x4+9x3
Question 4 (1 point)
What is the coefficient of the second term of the trinomial?

(4a+5)2=16a2+Ba+25
Question 4 options:

Question 5 (1 point)
Simplify.

(x−4)(x2−3x−9)
Question 5 options:

x3−7x2−21x+36

x3−7x2+3x+36

x3−4x2−12x+36

Answer 1

1)
`2y^(2)+4y-9`

2)
`18x^(5)y^(4)z`

3)
`6x^(5)-12x^(4)+9x^(3)`

4) 40

5)
`x^(3)-7x^(2)+3x+36`

Explanation:

1) Distribute the negative sign that is outside the parentheses and then you must add like terms, as following:

`(y^(2)-3y-5)-(-y^(2)-7y+4)=y^(2)-3y-5+y^(2)+7y-4=2y^(2)+4y-9`

2) According to the Product property of exponents, when you multiply powers with the same base, you must add the exponents. Then:

`(6xy^(3)z)(3x^(2)yx^(2))=18x^(5)y^(4)z`

3) Apply the Distributive property and the Product property of exponents. Then, you obtain:

`-3x^(3)(-2x^(2)+4x-3)=6x^(5)-12x^(4)+9x^(3)`

4)
`(4a+5)^(2)` is a square of a sum, then, by definition you have:

`(a+b)^(2)=a^(2)+2ab+b^(2)`

Then:

`(4a+5)^(2)=(4a)^(2)+2(4a)(5)+5^(2)=16a^(2)+40a+25`

The coefficient of the second term is the number in front of the variable a. Then, the answer is: 40

5) Apply the Distributive property and the Product property of exponents, then, oyou must add the like terms:

`(x-4)(x^(2)-3x-9)=x^(3)-3x^(2)-9x-4x^(2)+12x+36=x^(3)-7x^(2)+3x+36`