MATHEMATICS HIGH SCHOOL

(08.01, 08.02, 08.03, 08.05, 08.06 MC)Part A: Factor x2y2 + 6xy2 + 8y2. Show your work. (4 points)

Part B: Factor x2 + 8x + 16. Show your work. (3 points)

Part C: Factor x2 − 16. Show your work. (3 points)

Answers

Answer 1

Answer:

Answer: The factorization of all the parts are :

Part A : $x^2y^2+6xy^2+8y^2=y^2(x+2)(x+4).$

Part B : $x^2+8x+16=(x+4)(x+4).$

Part C : $x^2-16=(x+4)(x-4).$

Step-by-step explanation: We are given to factorize the following quadratic polynomials :

Part A : Factor x²y² + 6xy² + 8y².

Part B : Factor x² + 8x + 16.

Part C: Factor x² − 16.

We will be using the following factorization formulas :

$(i)~x^2+ax+bx+ab=(x+a)(x+b),\n\n(ii)~x^2+2xa+a^2=(x+a)^2=(x+a)(x+a),\n\n(iii)~x^2-a^2=(x+a)(x-a).$

The factorization of all the parts area as follows :

Part A :

We have

$x^2y^2+6xy^2+8y^2\n\n=y^2(x^2+6x+8)\n\n=y^2(x^2+4x+2x+8)\n\n=y^2(x(x+4)+2(x+4))\n\n=y^2(x+2)(x+4).$

So, $x^2y^2+6xy^2+8y^2=y^2(x+2)(x+4).$

Part B :

We have

$x^2+8x+16\n\n=x^2+2* x*4+4^2\n\n=(x+4)^2\n\n=(x+4)(x+4).$

So, $x^2+8x+16=(x+4)(x+4).$

Part C :

We have

$x^2-16\n\n=x^2-4^2\n\n=(x+4)(x-4).$

So, $x^2-16=(x+4)(x-4).$

Thus, all the parts are factorized.

Answer 2

Answer: is it x times 2 times y times 2? is that what it is asking or is it meaning squared

Related Questions

Write an explicit rule to represent the sequence :4, 10, 16, 22,...
Please help me thank u
Compare the method of using expanded form and the method of using place value to multiply a decimal and a whole number????
What is the coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin?
How much compound interest is earned on $4300 at 2.9% interest for 10 years, compounded quarterly?

Which of the following statements contains a quotient? A. 7 + 6 = 13 B. 7 × 6 = 42 C. 42 ÷ 6 = 7 D. 7 – 6 = 1

Answers

Mathematically, quotient means the solution you get when solving a division problem.

The only reliable choice is C)

Choice A) is called "the sum or total"
Choice B) is called "the product."
Choice D) is called the "the difference"

The quotient is the answer to a division problem. Therefore, C is the correct answer.

Can anyone explain how to solve this 5(6-2)^2-5

Answers

$5\cdot(6-2)^2-5=5\cdot4^2-5=5\cdot16-5=80-5=75$

Bob and his best friend Bill have the same birthday, but Bob is 3 years older than Bill. Let the variable x represent Bob’s age and y represent Bill’s age. Which equation models the relationship between Bill’s age and Bob’s age?a. y = x/3
b. y = x + 3
c. x = y + 3
d. y = 3x
Is the statement true or false? (ab)c = a(cb).
a. True
b. False

Answers

bob is 3 moer than bill
bob=3+bill
x=3+y
C is anre

second one
true, associative and commutative

C
A

Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. What is the value of a in the polynomial?

Answers

Answer:

product y ³ - 64 and a = 16.

Step-by-step explanation:

Given : (y — 4)(y² + 4y + 16) .

To find : Using the distributive property to find the product a polynomial of the form y³ + 4y² + ay – 4y² – ay – 64. What is the value of a in the polynomial?

Solution : We have given

(y — 4)(y² + 4y + 16) .

Distribute y over (y² + 4y + 16) and - 4 over (y² + 4y + 16).

y (y² + 4y + 16) - 4 (y² + 4y + 16).

y ³+ 4y² + 16 y - 4y² - 16y - 64.

This is in form of y³ + 4y² + ay – 4y² – ay – 64.

Here, a = 16.

Product : combine like terms

y ³+ 4y² - 4y² + 16y - 16y - 64.

y ³ - 64.

Therefore , product y ³ - 64 and a = 16.

it is 16 well I just draw it out and i got if

F(x)=x2−x−1f, left parenthesis, x, right parenthesis, equals, x, squared, minus, x, minus, 1 What is the average rate of change of fffover the interval -1\leq x\leq 1−1≤x≤1minus, 1, is less than or equal to, x, is less than or equal to, 1?

Answers

The average rate of change of f(x) over the interval -1 ≤ x ≤ 1 is -1.

Given the function $f(x) = x^2 - x - 1$ over the interval -1 ≤ x ≤ 1, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.

The value of f(x) at the endpoint x = -1:

f(-1) = (-1)² - (-1) - 1 = 1 + 1 - 1 = 1

Now, the value of f(x) at the endpoint x = 1:

f(1) = (1)² - (1) - 1 = 1 - 1 - 1 = -1

The difference in the function values is:

f(1) - f(-1) = -1 - 1 = -2

The difference in the x-values is:

1 - (-1) = 2

Now, we can calculate the average rate of change:

Average rate of change = (f(1) - f(-1)) / (1 - (-1)) = -2 / 2 = -1

Therefore, the average rate of change of f(x) over the interval -1 ≤ x ≤ 1 is -1.

Learn more about average rate;

brainly.com/question/20784578

#SPJ12

Answer:

ff has an average rate of change of zero over the interval

−

≤

�

≤

−1≤x≤2minus, 1, is less than or equal to, x, is less than or equal to, 2.

Step-by-step explanation:

-1≤x≤2

Find the volume of an object with a mass of 63 grams and a density of 9 g/cm

Answers

you have to divide it 63 divide by 9 = 7

Final answer:

To find the volume of an object, divide its mass by its density.

Explanation:

The volume of an object can be found by dividing its mass by its density. In this case, the mass is given as 63 grams and the density is given as 9 g/cm. To find the volume, divide the mass by the density: Volume = Mass / Density.

Substituting the given values, we get Volume = 63 g / 9 g/cm. Simplifying the equation, we find that the volume of the object is 7 cm³.