Question Simplify the expression $(30 a - 0.23 g)^2$ .

Studdy Solution

STEP 1

Assumptions
1. We need to simplify the expression $(30a - 0.23g)^2$ .
2. To do this, we will use the binomial square formula $(A - B)^2 = A^2 - 2AB + B^2$ , where $A = 30a$ and $B = 0.23g$ .

STEP 2

Apply the binomial square formula to the given expression.
$(30a - 0.23g)^2 = (30a)^2 - 2 \cdot (30a) \cdot (0.23g) + (0.23g)^2$

STEP 3

Square the first term $(30a)^2$ .
$(30a)^2 = 900a^2$

STEP 4

Multiply the terms for the middle part of the expression $-2 \cdot (30a) \cdot (0.23g)$ .
$-2 \cdot (30a) \cdot (0.23g) = -2 \cdot 30 \cdot 0.23 \cdot a \cdot g$

STEP 5

Calculate the numerical part of the middle expression.
$-2 \cdot 30 \cdot 0.23 = -13.8$

STEP 6

Combine the numerical part with the variables for the middle expression.
$-13.8 \cdot a \cdot g = -13.8ag$

STEP 7

Square the last term $(0.23g)^2$ .
$(0.23g)^2 = (0.23)^2 \cdot g^2$

STEP 8

Calculate the square of 0.23.
$(0.23)^2 = 0.0529$

STEP 9

Combine the numerical part with the variable for the last term.
$0.0529 \cdot g^2 = 0.0529g^2$

STEP 10

Now, combine all the parts to get the simplified expression.
$900a^2 - 13.8ag + 0.0529g^2$
The simplified expression is $900a^2 - 13.8ag + 0.0529g^2$ .

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