IDNLearn.com: Where your questions meet expert advice and community support. Our platform is designed to provide quick and accurate answers to any questions you may have.

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


Sagot :

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].