We Distribute, Yet Things Multiply

The distributive property turns products into sums. Four identities follow from it and make squaring and multiplying quick.

Key ideas

• Distributive property: a(b + c) = ab + ac, and (a + b)(c + d) = ac + ad + bc + bd.
• An identity is true for every value of the letters.
• A square of a sum or difference has three terms, not two.
• Quick squares: 99² = (100 − 1)² = 10 000 − 200 + 1 = 9801.
• Quick products: 52 × 48 = (50 + 2)(50 − 2) = 2500 − 4 = 2496.
• Areas show the identities: a square of side a + b splits into a², b² and two rectangles ab.

Remember

Watch out

• Writing (a + b)² = a² + b², leaving out 2ab.
• Getting the sign of the middle term wrong in (a − b)².
• Multiplying only the first terms of each bracket.

Worked example