Multiply: (1.5p – 0.5q) and (1.5p + 0.5q)

1.	Multiply: (1.5p – 0.5q) and (1.5p + 0.5q)
Answer» (1.5p – 0.5q) and (1.5p + 0.5q) = 1.5p (1.5p + 0.5q) – 0.5q (1.5p + 0.5q) = 1.5p × 1.5p + 1.5p × 0.5q – 0.5q × 1.5p – 0.5q × 0.5q = 1.5 × p × 1.5 × p + 1.5 × p × 0.5 × q – 0.5 × q × 1.5 × p – 0.5 × q × 0.5 × q = 1.5 × 1.5 × p × p + 1.5 × 0.5 × p × q – 0.5 × 1.5 × q × p – 0.5 × 0.5 × q × q = 2.25 × p² + 0.75 × pq – 0.75 × qp – 0.25 × q² = 2.25p² + 0.75pq – 0.75pq – 0.25q² = 2.25p² – 0.25q²

Answer»

(1.5p – 0.5q) and (1.5p + 0.5q)

= 1.5p (1.5p + 0.5q) – 0.5q (1.5p + 0.5q)

= 1.5p × 1.5p + 1.5p × 0.5q – 0.5q × 1.5p – 0.5q × 0.5q

= 1.5 × p × 1.5 × p + 1.5 × p × 0.5 × q – 0.5 × q × 1.5 × p – 0.5 × q × 0.5 × q

= 1.5 × 1.5 × p × p + 1.5 × 0.5 × p × q – 0.5 × 1.5 × q × p – 0.5 × 0.5 × q × q

= 2.25 × p² + 0.75 × pq – 0.75 × qp – 0.25 × q²

= 2.25p² + 0.75pq – 0.75pq – 0.25q²

= 2.25p² – 0.25q²

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