Question

Simplify: (2.5a-1.5b)^2-(1.5a-2.5b)^2​

Answer 1

Answer:

⇢ ${\boxed{\sf{4a^{2} + -4b^{2}}}}$

Step-by-step explanation:

$\sf{\longrightarrow (2.5a - 1.5b)^{2} - (1.5a - 2.5b)^{2}}$

ㅤ

$\sf{\longrightarrow 6.25a^{2} + -7.5ab + 2.25b^{2} + -2.25a^{2} + 7.5ab + -6.25b^{2}}$

ㅤ

$\sf{\longrightarrow (6.25a^{2} + -2.25a^{2}) + (-7.5ab + 7.5ab) + (2.25b^{2} +-6.25b^{2})}$

ㅤ

⇢ ${\boxed{\sf{4a^{2} + -4b^{2}}}}$

ㅤ

Therefore, this is the required answer.

Additional explanation:

★ To simplify equations, we have to do two important steps:

ㅤ

1) Disturbing the given equation.

2) Combining the like terms.

Answer 2

Answer:

2.5a−1.5b)

2

−(1.5a−2.5b)

2

Evaluate the power

4

25a

2

−

2

15ab

+

4

9b

2

−(1.5a−2.5b)

2

Evaluate the power

4

25a

2

−

2

15ab

+

4

9b

2

−(

4

9a

2

−

2

15ab

+

4

25b

2

)

Rewrite the expression

4

25a

2

−

2

15ab

+

4

9b

2

−

4

9a

2

+

2

15ab

−

4

25b

2

Reduce fractions to a common denominator

4

25a

2

−

2×2

15ab×2

+

4

9b

2

−

4

9a

2

+

2×2

15ab×2

−

4

25b

2

Reorder the terms

4

25a

2

−

4

30ab

+

4

9b

2

−

4

9a

2

+

4

30ab

−

4

25b

2

Add the terms

4

25a

2

−30ab+9b

2

−9a

2

+30ab−25b

2

Calculate

4

16a

2

−16b

2

Solution

4a

2

−4b

2