81a2 + 36a + 4 factor
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factor 81a^2 + 36a + 4
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SOLUTION: Please help, factor the expression 81a^2-36ab+4b^2 ...
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81a^2+36a+4
To factor the expression 81a^2 + 36a + 4, we need to identify any common factors and then apply a factoring method. In this case, the expression does not have any common factors other than 1.
To factor a quadratic expression, we can use the factoring by grouping method. Here's how you can do it:
Step 1: Multiply the coefficient of the squared term (81) by the constant term (4). In this case, 81 * 4 = 324.
Step 2: Find two numbers whose product is equal to 324 and whose sum is equal to the coefficient of the linear term (36). In this case, the numbers are 18 and 18 since 18 * 18 = 324 and 18 + 18 = 36.
Step 3: Rewrite the middle term (36a) using the two numbers found in step 2. Split the middle term into two terms using the same numbers. The expression becomes:
81a^2 + 18a + 18a + 4
Step 4: Group the terms in pairs and factor out the greatest common factor (GCF) for each pair separately. For the first pair, the GCF is 9a, and for the second pair, the GCF is 2:
(81a^2 + 18a) + (18a + 4)
Step 5: Factor out the GCF from each pair:
9a(9a + 2) + 2(9a + 2)
Step 6: Notice that the terms in parentheses are the same, so factor out the common binomial factor:
(9a + 2)(9a + 2)
Step 7: Simplify the expression:
(9a + 2)^2
Therefore, the factored form of the expression 81a^2 + 36a + 4 is (9a + 2)^2.