Write this expression in expanded form. 4(a-b)2
4(a^2-2ab+b^2)
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To expand the expression 4(a - b)^2, we need to perform the squaring operation on the quantity (a - b) first, and then multiply the result by 4.
The square of (a - b) is (a - b)(a - b), which can be expanded using the FOIL method. This gives us:
(a - b)(a - b) = a^2 - ab - ba + b^2
Simplifying further, we combine like terms:
= a^2 - 2ab + b^2
Finally, we multiply the expression above by 4:
4(a - b)^2 = 4(a^2 - 2ab + b^2)
Therefore, the expanded form of the expression 4(a - b)^2 is 4a^2 - 8ab + 4b^2.
To expand the expression 4(a-b)^2, we can use the distributive property. Let's break down the steps:
Step 1: Start with the expression 4(a-b)^2.
Step 2: Rewrite (a-b)^2 as (a-b)(a-b) using the exponent rule for squaring.
Step 3: Apply the distributive property to each term in the expression. Multiply 4 by both terms inside the parentheses.
Step 4: Simplify the expression by multiplying the terms.
Step 5: Combine like terms, if any.
Let's go through the steps one by one:
Step 1: Start with the expression 4(a-b)^2.
Step 2: Rewrite (a-b)^2 as (a-b)(a-b):
4(a-b)(a-b)
Step 3: Apply the distributive property:
4(a*a - a*b - b*a + b*b)
Step 4: Simplify by multiplying:
4(a^2 - 2ab + b^2)
Step 5: Combine like terms, if any:
4a^2 - 8ab + 4b^2
Therefore, the expanded form of the expression 4(a-b)^2 is 4a^2 - 8ab + 4b^2.