1. (x + 2y)^2 = x^2 + ___ + 4y^2 2. (2x – 5y)^2 = __ – 20xy + __

Question

Use the formulae to fill proper terms in the following boxes.

1. (x + 2y)² = x² + ___ + 4y² 

2. (2x – 5y)² = __ – 20xy + __ 

3. (101)² = (100 + 1)² = ___+ ___ + 1² = ___ 

4. (98)² = (100 – 2)²= 10000 – ___ + ___ = ___ 

5. (5m + 3n) (5m – 3n) = ___ – ___ = ___ – __

Answer 1

1. (x + 2y)² = x² + 4xy + 4y² 

2. (2x – 5y)² = 4x² – 20xy + 25y²

3. (101)² = (100 + 1)² = 10000+ 200 + 1² = 10201 

4. (98)² = (100 – 2)²= 10000 – 400 + 4 = 9604

5. (5m + 3n) (5m – 3n) = (5m)² – (3n)² = 25m² – 9n²

Answer 2

1. (x+2y)²=x²+2×x×2y+(2y)²=x²+4xy+4y² (Use this formula (a+b)²=a²+2ab+b²)
2. (2x – 5y)²=4x²-20xy+25y² (Use this formula (a-b)²=a²-2ab+b²)
3. (101)²=(100+1)²=(100)²+2×100×1+1=10000+200+1=10201(Same formula for it)
4. (98)²=(100-2)²=10000-2×100×2+4=10004-400=9604 (Same formula use for it)
5. (5m+3n)(5m-3n)=(5m)²-(3n)²=25m²-9n²

(Use the formula a²-b²=(a+b)(a-b)

Hope you clearly understood this, through the basics formula of alzebra)