Products And Powers Algebra
The system of relations and operations, and the constructions and concepts arising from them
, equations, algebraic structures including terms, and polynomials are using in algebra. Mathematics contains some main parts; one of the main branches is algebra.
Algebra performs some arithmetic operation, products and powers problem also handle this chapter. Algebra problems use some variables like x, y, and z. and also using variables and signs. This article we are discussing about problems for products and powers in algebra.
In algebra, the results in the problems are generally provided with accurate or non-accurate manner. Some problems give the answers with non-accuracy and some with accuracy.Some problems are involved in the logarithmic terms that does not provide accurate values in the answers when we find the logarithmic values for the functions.
Examples Problem for Products in Algebra:
1. Solve the products problem, given values is (p + 4) (p + 6)
Solution:
= (p +4) (p + 6)
Multiply the two terms and combine the terms,
= (p^2 + 4 + 6) p + 4 6
Then we get the solution is,
= p^2 + 10p + 24
2. Solve the products problem, given values is (x + 6) (x 5)
Solution:
= (x + 6) (x 5)
Multiply the two terms and combine the terms,
= x^2 -5x + 6x 30
Then we get the solution is,
= x^2 + 1x- 30
3. Solve the products problem, given values is (y 8 (y 5)
Solution:
= (y 8) (y 5)
Multiply the two terms and combine the terms,
= y^2 -5y -8y + 40
Then we get the solution is,
= y^2 13y + 40
4. Solve the products problem, given values is (a 5) (a + 2)
Solution:
= (a 5) (a + 2)
Multiply the two terms and combine the terms,
= a^2 + 2a 5a 10
Then we get the solution is,
= a^2 3a 10
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Examples Problem for Powers in Algebra:
1. Solve the powers problem, given values is (i) (2a + b + 2c) 2
Solution:
= (2a + b + 2c)^2
= [(2a) + b + (2c)]2
= (2a)^2 + b^2 + (2c)^2 + 2(2a)b + 2b (2c) + 2(2c) (2a)
= 4a^2 + b^2 + 4c^2 + 4ab + 4bc + 8ca.
2. Solve the powers problem, given values is (2x + 5y)^2
Solution:
= (2x + 5y)^2 (using (a +b)^2 = a^2 + 2ab + b^2)
= (2x)^2 + 2(2x) (5y) + (5y)^2
= 4x^2+ 20xy + 25y^2.
Practice problems for products and powers in algebra:
1. Solve the products problem, given values is (x + 2) (x + 2)
Solution is x^2 + 4x + 2
2. Solve the products problem, given values is (y + 8) (y + 6)
Solution is y^2 + 14y + 48
3. Solve the products problem, given values is (x 7) (x + 3)
Solution is x^2 -4x -21.
4. Solve the powers problem, given values is (4x + 4y) 2
Solution is 16x^2 +32xy + 16y^2
5.Solve the powers problem, given values is (10x + 9y) 2
Solution is 100x^2 + 180xy + 81y^2
by: nitinp
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