Factor the expression below 36a2-25b2 which binomial is factor of the expression

Mathematics

2 answers:

Serhud [2]3 years ago

7 0

Answer: (6a + 5b) • (6a - 5b)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b2" was replaced by "b^2". 1 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(36 • (a2)) - 52b2

Step 2 :

Equation at the end of step 2 :

(22•32a2) - 52b2

Step 3 :

Trying to factor as a Difference of Squares :

3.1 Factoring: 36a2-25b2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 36 is the square of 6

Check : 25 is the square of 5

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (6a + 5b) • (6a - 5b)

Final result :

(6a + 5b) • (6a - 5b)

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alukav5142 [94]3 years ago

6 0

Answer: 6a + 5b

Step-by-step explanation:

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Factoring trinomials

Tcecarenko [31]

$c^2$ $2c^2 + 13c +21 \\4c^2 + 13(2)c + 42\\(2c + 6)(2c+7)\\(c+3)(2c+7)$

This is a way to factoring trinomials (there exist different equivalent methods).

Multiply the trinomial but the term accompanying $c^2$ . This is the second line. Then, you could take the square of the $4c^2$ , ant try to create a factor () () that will correspond to the expression in the second line. That is, we want $4c^2 + 13(2) c + 42 = (2c + ?) (2c + ?)$

In ? we put the corresponding numbers that, if we multiply them we will obtain 42, and if we add them we will obtain 13. This numbers are 6 and 7. Then, we have $(2c + 6) (2c +7)$