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When we encounter a multiplication exercise of this type, we know that we must use the distributive property.
Step 1: Multiply the first factor of the first parentheses by each of the factors of the second parentheses.
Step 2: Multiply the second factor of the first parentheses by each of the factors of the second parentheses.
Step 3: Group like terms.
a * (c+3) =
a*c + a*3
4 * (c+3) =
4*c + 4*3
ac+3a+4c+12
There are no like terms to simplify here, so this is the solution!
\( (3+20)\times(12+4)= \)
Each of the 2 terms in the first binomial must multiply each of the 2 terms in the second binomial. That's 2 × 2 = 4 multiplication operations, giving you 4 terms total!
FOIL is just a memory trick for the distributive property! It helps you remember: First, Outer, Inner, Last terms. Both methods give the same answer.
No! is the same as . The order doesn't matter as long as you have all 4 terms.
Count your terms! You should have exactly 4 terms when multiplying two binomials. Also, substitute simple numbers like a=1, c=1 to verify: (1+4)(1+3) = 5×4 = 20, and 1+3+4+12 = 20 ✓
In this problem, no terms can be combined because ac, 3a, 4c, and 12 are all different types. Only combine terms with exactly the same variables and exponents!
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