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alekssr [168]
2 years ago
14

Find an expression which represents the sum of (7x-y)(7x−y) and (5x+3y)(5x+3y) in simplest terms.

Mathematics
1 answer:
lisov135 [29]2 years ago
8 0

Answer:

Hello,

Step-by-step explanation:

(7x - y)(7x - y) + (5x+3y)(5x+3y)\\\\=(7x-y)^2+(5x+3y)^2\\=(49x^2-14xy+y^2)+(25x^2+30xy+9y^2)\\\\\boxed{=74x^2+16xy+10y^2}

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There are several ways two triangles can be congruent.

  • \mathbf{AC = BD}<em> congruent by SAS</em>
  • \mathbf{\angle ABC \cong \angle BAD}<em> congruent by corresponding theorem</em>

In \mathbf{\triangle AOL} and \mathbf{\triangle BOK} (see attachment), we have the following observations

1.\ \mathbf{AO = DO} --- Because O is the midpoint of line segment AD

2.\ \mathbf{BO = CO} --- Because O is the midpoint of line segment BC

3.\ \mathbf{\angle AOB =\angle COD} ---- Because vertical angles are congruent

4.\ \mathbf{\angle AOC =\angle BOD} ---- Because vertical angles are congruent

Using the SAS (<em>side-angle-side</em>) postulate, we have:

\mathbf{AC = BD}

Using corresponding theorem,

\mathbf{\angle ABC \cong \angle BAD} ---- i.e. both triangles are congruent

The above congruence equation is true because:

  1. <em>2 sides of both triangles are congruent</em>
  2. <em>1 angle each of both triangles is equal</em>
  3. <em>Corresponding angles are equal</em>

See attachment

Read more about congruence triangles at:

brainly.com/question/20517835

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