Question

Replace ∗ with a monomial to obtain an identity:

1. (∗− 2m)^2 = 100–40m+4m^2

2. (3a+2.5b)^2=9a^2+6.25b^2 + ∗

Answer 1

1. ∗ = 10

2. ∗ = 15ab

Explanation:

The identity: (A-B)²=A²-2AB+B² or (A+B)²= A²+2AB+B²

1. In the first problem, A = ∗, which means that ∗² is going to be equal to 100.

∗ = √100= 10

2. In the second problem we already have A and B, and we have both A² (9a²) and B² (6.25b²) and we are missing the "2AB" part in the middle.

∗ = 2AB = 2×3a×2.5b = 15ab