Question

Factorize the following:
28a² + 14a²b² − 21a⁴

Answer 1

\[\text{ The greatest common factor of the terms }28 a^2 , 14 a^2 b^2\text{ and }21 a^4\text{ of the expression }28 a^2 + 14 a^2 b^2 - 21 a^4 is 7 a^2 . \]
\[\text{ Also, we can write }28 a^2 = 7 a^2 \times 4, 14 a^2 b^2 = 7 a^2 \times 2 b^2\text{ and }21 a^4 = 7 a^2 \times 3 a^2 . \]
\[ \therefore 28 a^2 + 14 a^2 b^2 - 21 a^4 = 7 a^2 \times 4 + 7 a^2 \times 2 b^2 - 7 a^2 \times 3 a^2 \]
\[ = 7 a^2 (4 + 2 b^2 - 3 a^2 )\]