Please help Adding/Subtracting Polynomials

1. (a^2 + ab – 3b^2) + (4a^2 – ab + b^2)

2. (7a^2–a+4)–(3a^2–4a–3)

3. (5e^2–e–7)–(-2e^2+3e+4)

Multiplying Polynomials

4. 4a(3x+5)

5. 6rs(2r^2+3rs)

6. 3x(5x^2–x+4)

7. (a+b)(2a–3b)

8. (z–2x)(z–2x)

9. (2y+3)(y^2+3y–6) 10.(e – f)(e^2 – 2ef + f^2)

How would we know.

Hope this helps!

all are a polynomial function and

1.the degree is 3 and number of term is 4

2. 1 and 3

3. 1 and 4/3

4. 2 and -4

5. 2 and 1

12x² - 6x + 13

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/Coefficients/Degrees

Step-by-step explanation:

Step 1: Set up

(9x² - 4x + 11) + (3x² - 2x + 2)

Step 2: Simplify

Combine like terms (x²): 12x² - 4x + 11 - 2x + 2Combine like terms (x): 12x² - 6x + 11 + 2Combine like terms (Z): 12x² - 6x + 13

9.32/le4

Step-by-step explanation:

[tex]1.\\(4x^2+15x-3)-(-3x^2+5)\\=4x^2+15x-3+3x^2-5\\=7x^2+15x-8\leftarrow A.[/tex]

[tex]2.\\-3f^2+4f-3+8f^2+7f+1\\=5f^2+11f-2\leftarrow C.[/tex]

[tex]3.\\(2x^2+6x+1)+(-7x^2+2x-3)\\=2x^2+6x+1-7x^2+2x-3\\=-5x^2+8x-2\leftarrow B.[/tex]

[tex]4.\\4x^2+3x-3\\\{4;\ 3;-3\}[/tex]

[tex]5.\\6x^4+3x^3-2x^2+15x-14\\\{6;\ 3;-2;\ 15;-14\}\to5\leftarrow A.[/tex]

[tex]6.\\-7x-5x^2+5\\\{-7\}\leftarrow D.[/tex]

[tex]7.\\(2.5\cdot10^4)(4\cdot10^3)=2.5\cdot4\cdot10^{4+3}=10\cdot10^7\\=10^{1+7}=10^8=1\cdot10^8\leftarrow C.[/tex]

[tex]8.\\2^2\cdot2^8=2^{2+8}=2^{10}\leftarrow B.[/tex]

13

Step-by-step explanation:

q-7 can go into 13q-91 thirteen times.

Set up the long division sign with the q-7 on the outside and the 13q-91 inside.

Then, notice that to get to 13, you multiply the q and 7 by 13. This gets both terms to 13q and 91, which cancel out the numbers inside the long division sign.

(1) A

(2) C

(3) B

(4) The coefficients are 4,3,-3.

(5) A

(6) D

(7) C

(8) B

Step-by-step explanation:

(1)

The given expression is

[tex](4x^2 + 15x - 3) - (-3x^2 + 5)[/tex]

Using distributive property.

[tex](4x^2 + 15x - 3) - (-3x^2) -( 5)[/tex]

[tex]4x^2 + 15x - 3 + 3x^2 - 5[/tex]

On combining like terms.

[tex](4x^2+3x^2) + 15x +(- 3 - 5)[/tex]

[tex]7x^2 + 15x-8[/tex]

Therefore, the correct option is A.

(2)

The given expression is

[tex]-3f^2 + 4f - 3 + 8f^2 + 7f + 1[/tex]

On combining like terms.

[tex](-3f^2+ 8f^2) +( 4f + 7f )+(- 3 + 1)[/tex]

[tex]5f^2 +11f -2[/tex]

Therefore, the correct option is C.

(3)

The given expression is

[tex](2x^2 + 6x + 1) + (-7x^2 + 2x - 3)[/tex]

Combined like terms.

[tex](2x^2-7x^2) + (6x+ 2x) + (1 - 3)[/tex]

[tex]-5x^2 + 8x -2[/tex]

Therefore, the correct option is B.

(4)

The given expression is

[tex]4x^2 + 3x - 3[/tex]

A number before variable terms are called coefficient of that term.

Therefore, the coefficients are 4,3,-3.

(5)

The given expression is

[tex]6x^4 + 3x^3 - 2x^2 + 15x - 14[/tex]

It this polynomial, the number of terms is 5.

Therefore the correct option is A.

(6)

The given expression is

[tex]-7x - 5x^2 + 5[/tex]

The coefficient to x is -7.

Therefore, the correct option is D.

(7)

The given expression is

[tex](2.5\cdot 10^4)(4\cdot 10^3)[/tex]

[tex](2.5\cdot 4)\cdot (10^4\cdot 10^3)[/tex]

Using product property of exponent.

[tex](10)\cdot 10^{4+3}[/tex]

[tex]1\cdot 10^{1+4+3}[/tex]

[tex]1\cdot 10^{8}[/tex]

Therefore, the correct option is C.

(8)

The given expression is

[tex]2^2\cdot 2^8[/tex]

Using product property of exponent.

[tex]2^{2+8}[/tex]

[tex]2^{10}[/tex]

Therefore, the correct option is B.

972

Step-by-step explanation:

The first term is (9x)^3, so the coefficient of x is 9. Since the degree is 3, the second term must have a multiplier of (3 choose 1). 1458 / (3 choose 1) = 486.

486 / (9^2) = 6. Therefore, the coefficient of y must be 6. Since the second term is negative, the coefficient of y is also negative. Thus, this can be written as (9x-6y)^3. Solving for the xy^2 term gives us (3 choose 2) * 9 * 6^2 = [tex]\boxed{972}[/tex] or the third option.

27x4−30x3+59x2−30x+22

Step-by-step explanation:

c

Step-by-step explanation: