(3a+2b-1)(a+5)-2b(a-2)=(3a+5)(a+3)+2(7b-10)

2 min read Jun 16, 2024

Solving the Equation: (3a+2b-1)(a+5)-2b(a-2)=(3a+5)(a+3)+2(7b-10)

This article will guide you through the steps of solving the given equation:

(3a+2b-1)(a+5)-2b(a-2)=(3a+5)(a+3)+2(7b-10)

1. Expand both sides of the equation:

Left side:
- (3a+2b-1)(a+5) = 3a² + 15a + 2ab + 10b - a - 5
- -2b(a-2) = -2ab + 4b
Right side:
- (3a+5)(a+3) = 3a² + 9a + 5a + 15
- 2(7b-10) = 14b - 20

2. Combine like terms on both sides:

3. Simplify the equation:

Now, the equation becomes:

3a² + 14a + 14b - 5 = 3a² + 14a + 14b - 5

4. Observe the result:

We can see that both sides of the equation are identical. This means that the equation is true for all values of a and b.

Conclusion:

The given equation is an identity. This means that it is true for any values of the variables a and b.