8a^2 + 40ab+ 50b^2 =
To solve the equation 8a^2 + 40ab + 50b^2 = 0, you can use the factoring method.
Step 1: Observe the expression 8a^2 + 40ab + 50b^2 and look for any common factors among the terms. In this case, there are no common factors among the coefficients 8, 40, and 50.
Step 2: Look for two binomials that, when multiplied together, result in the given expression. The pattern for factoring a quadratic trinomial is (ma + nb)(pa + qb), where m, n, p, and q are the coefficients.
Given: 8a^2 + 40ab + 50b^2
Now, we need to find values for m, n, p, and q such that when we multiply (ma + nb)(pa + qb), we get the given expression.
Step 3: Split the middle term (40ab) into two terms whose coefficients multiply to give us 8 * 50 = 400 and whose coefficients add up to the coefficient of the middle term (40). The two terms are 10ab and 30ab.
Now, we can write the expression as follows:
8a^2 + 10ab + 30ab + 50b^2
Step 4: Group the terms and factor by grouping:
(8a^2 + 10ab) + (30ab + 50b^2)
2a(4a + 5b) + 10b(3a + 5b)
Step 5: Observe that we now have two common binomial factors, (4a + 5b) and (3a + 5b).
Now, we can write the equation as:
2a(4a + 5b) + 10b(3a + 5b) = 0
Step 6: Apply the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
So either 2a = 0 or (4a + 5b) = 0
And either 10b = 0 or (3a + 5b) = 0
Solving these equations will give us the values of a and b that satisfy the equation 8a^2 + 40ab + 50b^2 = 0.