Skip to content
Practice Problems

A Comprehensive Guide To Polynomial Operations, Coordinate Geometry, And Mathematical Simplification

Simplify your math studies with this detailed Homework Solution.

Preview 4 of 10 pages

See the first 4 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    A Comprehensive Guide to Polynomial Operations, Coordinate Geometry, and Mathematical Simplification Polynomials and Mathematical Simplification: A Step - by - Step Approach (10x + 12) + (6x + 10) add the polynomial Let's break down the given expression step by step: Given: (10x+12)+(6x+10)(10x + 12) + (6x + 10) Step 1: Remove the parentheses Since there are no negative signs outside the parentheses, we can directly combine the terms inside the parentheses. 10x+12+6x+1010x + 12 + 6x + 10 Step 2: Combine like terms Now, group the like terms (terms involving xx and constant terms): • Combine the xx - terms: 10x+6x=16x10x + 6x = 16x • Combine the constants: 12+10=2212 + 10 = 22 Step 3: Write the simplified result So, the simplified expression is: 16x+2216x + 22 Final Answer: 16x+2216x + 22 2. Subtract the polynomial Let's break down the given expression step by step: Given: (11x2+7x+11)−(11x2+20x+12)(11x^2 + 7x + 11) - (11x^2 + 20x + 12) Step 1: Distribute the negative sign

  2. Page 2
  3. Page 3
    Read page 3 as text

    Distribute the negative sign across the second set of parentheses: 11x2+7x+11−11x2−20x−1211x^2 + 7x + 11 - 11x^2 - 20x - 12 Step 2: Combine like terms Now, group the like terms (terms involving x2x^2, xx, and constants): • Combine the x2x^2 - terms: 11x2−11x2=011x^2 - 11x^2 = 0 • Combine the xx - terms: 7x−20x=−13x7x - 20x = - 13x • Combine the constant terms: 11−12=−111 - 12 = - 1 Step 3: Write the simplified result So, the simplified expression is: −13x−1 - 13x - 1 Final Answer: −13x−1 - 13x - 1 3. Simplify Let's simplify 12×14412 \ times \ sqrt{144}. Step 1: Find the square root of 144 144=12 \ sqrt{144} = 12 Step 2: Multiply by 12

  4. Page 4
    Read page 4 as text

    12×12=14412 \ times 12 = 144 Final Answer: 144144 4. Find the distance between P and Q using the distance formula P( - 3,8) and Q(5,8) To find the distance between the points P(−3,8)P( - 3, 8) and Q(5,8)Q(5, 8) using the distance formula, we'll follow the steps below: Distance Formula: The formula is: d=(x2−x1)2+(y2−y1)2d = \ sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Where: • (x1,y1)(x_1, y_1) is the first point (P), • (x2,y2)(x_2, y_2) is the second point (Q). Step 1: Identify the coordinates of points P and Q • P(x1,y1)=(−3,8)P(x_1, y_1) = ( - 3, 8) • Q(x2,y2)=(5,8)Q(x_2, y_2) = (5, 8) Step 2: Plug the coordinates into the distance formula Now substitute the values of x1x_1, y1y_1, x2x_2, and y2y_2 into the formula: d=(5−(−3))2+(8−8)2d = \ sqrt{(5 - ( - 3))^2 + (8 - 8)^2} Step 3: Simplify the terms First, simplify inside the parentheses:

6 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Mathematics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.