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].
