NCERT Figure it Out 1 - Q5 - We Distribute, Yet Things Multiply
Question: Expand (i) (a - b)(a + b), (ii) (a - b)(a^2 + ab + b^2), (iii) (a - b)(a^3 + a^2b + ab^2 + b^3). Spot the pattern and state the next identity.
Answer: (i) a^2-b^2 (ii) a^3-b^3 (iii) a^4-b^4; next: (a-b)(sum a^{4-k}b^k)=a^5-b^5.
Full step-by-step NCERT solution with diagrams on Something by Zero.