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IrinaK [193]
2 years ago
10

Use any method to multiply (3a + 2b - c)(a - b + 2c).​

Mathematics
1 answer:
Alla [95]2 years ago
6 0

Answer: 3a^{2}-ab + 5ac- 2b^{2} + 5bc-2c^{2}

Step-by-step explanation:

(3a + 2b − c) (a − b + 2c)  

Expand (3a + 2b − c) (a − b + 2c) by multiplying each  term in the first  expression by each  term in the second expression.

3a ⋅ a + 3a (−b) + 3a (2c) + 2ba + 2b (−b) + 2b (2c) − ca − c (−b) − c (2c)

3 (a ⋅ a) + 3a (−b) + 3a (2c) + 2ba + 2b (−b) + 2b (2c) − ca − c (−b) − c (2c)

3a^2 + 3a (−b) + 3a (2c) + 2ba + 2b (−b) + 2b (2c) − ca − c (−b) − c (2c)

Rewrite using the commutative property of multiplication.

3a^2 + 3 ⋅ −1ab + 3a (2c) + 2ba + 2b (−b) + 2b (2c) − ca − c (−b) − c (2c)

3a^2 − 3ab + 3a (2c) + 2ba + 2b (−b) + 2b (2c) − ca − c (−b) − c (2c)

Rewrite using the commutative property of multiplication.

3a^2 − 3ab + 3 ⋅ 2ac + 2ba + 2b (−b) + 2b (2c) − ca − c (−b) − c (2c)

3a^2 − 3ab + 6ac + 2ba + 2b (−b) + 2b (2c) − ca − c (−b) − c (2c)

Rewrite using the commutative property of multiplication.

3a^2 − 3ab + 6ac + 2ba + 2 ⋅ −1b ⋅ b + 2b (2c) − ca − c (−b) − c (2c)

3a^2 − 3ab + 6ac + 2ba + 2 ⋅ −1 (b ⋅ b) + 2b (2c) − ca − c (−b) − c (2c)

3a^2 − 3ab + 6ac + 2ba + 2 ⋅ −1b^2 + 2b (2c) − ca − c (−b) − c (2c)

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 2b (2c) − ca − c (−b) − c (2c)

Rewrite using the commutative property of multiplication.

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 2 ⋅ 2bc − ca − c (−b) − c (2c)

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca − c (−b) − c (2c)

Rewrite using the commutative property of multiplication.

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca − 1 ⋅ −1cb − c (2c)

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca + 1cb − c (2c)

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca + cb − c (2c)

Rewrite using the commutative property of multiplication.

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca + cb − 1 ⋅ 2c ⋅ c

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca + cb − 1 ⋅ 2 (c ⋅ c)

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca + cb − 1 ⋅ 2c^2

3a^2 − 3ab + 6ac + 2ba − 2b^2 + 4bc − ca + cb − 2c^2

3a^2 − 3ab + 2ab + 6ac − 2b^2 + 4bc − ca + cb − 2c^2

3a^2 − ab + 6ac − 2b^2 + 4bc − ca + cb − 2c^2

3a^2 − ab − 2b^2 + 4bc + 6ac − 1ac + cb − 2c^2

3a^2 − ab − 2b^2 + 4bc + 5ac + cb − 2c^2

3a^2 − ab − 2b^2 + 4bc + bc + 5ac − 2c^2

3a^2 − ab − 2b^2 + 5bc + 5ac − 2c^2

3a^2 − ab − 2b^2 + 5ac + 5bc − 2c^2

3a^2 − ab + 5ac − 2b^2 + 5bc − 2c^2

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Please Help Me!
alex41 [277]

Answer:

✔️2 sets of corresponding angles

<D and <S

<R and <L

✔️2 sets of corresponding sides

DR and SL

RM and LT

Step-by-step explanation:

When two polygons are congruent, it implies that they have the same shape and size. Therefore, their corresponding angles and sides are congruent to each other.

When naming congruent polygons, the arrangement of the vertices are kept in a definite order of arrangement.

Therefore, Given that polygon DRMF is congruent to SLTO, the following angles and sides correspond to each other:

<D corresponds to <S

<R corresponds to <L

<M corresponds to <T

<F corresponds to <O

For the sides, we have:

DR corresponds to SL

RM corresponds to LT

MF corresponds to TO

FD corresponds to OS.

We can select any two out of these sets of corresponding angles and sides as our answer. Thus:

✔️2 sets of corresponding angles

<D and <S

<R and <L

✔️2 sets of corresponding sides

DR and SL

RM and LT

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