Questions: (5c-4d)^2

Transcript text: $(5c-4d)^{2}$

Solution

Solution Steps

To solve the expression $(5c - 4d)^2$, we need to expand it using the formula for the square of a binomial: $(a - b)^2 = a^2 - 2ab + b^2$.

Step 1: Expand the Expression

To expand the expression $(5c - 4d)^2$, we apply the binomial expansion formula: \[ (a - b)^2 = a^2 - 2ab + b^2 \] Here, $a = 5c$ and $b = 4d$. Thus, we have: \[ (5c - 4d)^2 = (5c)^2 - 2(5c)(4d) + (4d)^2 \]

Step 2: Calculate Each Term

Calculating each term separately:

$(5c)^2 = 25c^2$
$-2(5c)(4d) = -40cd$
$(4d)^2 = 16d^2$

Combining these results gives: \[ (5c - 4d)^2 = 25c^2 - 40cd + 16d^2 \]

Step 3: Substitute Values

Substituting $c = 1$ and $d = 1$ into the expanded expression: \[ 25(1)^2 - 40(1)(1) + 16(1)^2 = 25 - 40 + 16 \]

Step 4: Simplify the Expression

Now, simplifying the expression: \[ 25 - 40 + 16 = 1 \]

Final Answer

The final result of the expression $(5c - 4d)^2$ when $c = 1$ and $d = 1$ is: \[ \boxed{1} \]

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