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

Answer:

1) $2y^{2}+4y-9$

2) $18x^{5}y^{4}z$

3) $6x^{5}-12x^{4}+9x^{3}$

4) 40

5) $x^{3}-7x^{2}+3x+36$

Step-by-step 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:

$(x-4)(x^{2}-3x-9)=x^{3}-3x^{2}-9x-4x^{2}+12x+36=x^{3}-7x^{2}+3x+36$