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Evaluate the following by using identities:
[tex]\[ 0.54 \times 0.54 - 0.46 \times 0.46 \][/tex]

Sagot :

GinnyAnswer
To solve the expression [tex]\(0.54 \times 0.54 - 0.46 \times 0.46\)[/tex] using identities, we can use the difference of squares identity. The difference of squares identity states that:

[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]

Here, we have:
- [tex]\(a = 0.54\)[/tex]
- [tex]\(b = 0.46\)[/tex]

Step-by-step solution:

1. Identify the terms: Let [tex]\(a = 0.54\)[/tex] and [tex]\(b = 0.46\)[/tex].

2. Calculate [tex]\(a + b\)[/tex]:
[tex]\[ a + b = 0.54 + 0.46 = 1.0 \][/tex]

3. Calculate [tex]\(a - b\)[/tex]:
[tex]\[ a - b = 0.54 - 0.46 = 0.08 \][/tex]

4. Apply the difference of squares identity:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]

5. Substitute the calculated values:
[tex]\[ 0.54^2 - 0.46^2 = (0.08)(1.0) \][/tex]

6. Calculate the final result:
[tex]\[ 0.08 \times 1.0 = 0.08000000000000002 \][/tex]

Therefore, the value of [tex]\(0.54 \times 0.54 - 0.46 \times 0.46\)[/tex] is [tex]\(0.08000000000000002\)[/tex].
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