Please helpAdding/Subtracting Polynomials1. (a^2 + ab – 3b^2) + (4a^2 – ab + b^2)2. (7a^2–a+4)–(3a^2–4a–3)3.

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)

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This Post Has 10 Comments

  1. 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

  2. 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

  3. [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]

  4. 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.

  5. (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.

  6. 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.

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