A large square with side (a+b) is divided into four regions to show why (a+b)² equals a² + 2ab + b². Shallow 3D tiles in blue and turquoise represent the a² square, the two equal ab rectangles, and the b² square, fitting together without gaps. Useful for students learning algebraic identities and for teachers introducing area-based proofs before symbolic manipulation.
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Create a premium 15-second educational animation explaining the square of a sum through geometric areas: (a+b)² = a² + 2ab + b² FORMAT AND STYLE Vertical 9:16, 1080 × 1920. Elegant, clean educational motion design. Geometry must be the main focus; keep text minimal. Use shallow 3D tiles with a straight-on camera so the shapes and their areas remain mathematically clear. Soft studio lighting, subtle shadows, smooth movement and generous empty space. COLOR PALETTE — ICE BLUE Background: #F3F8FC, with a very soft ice-blue gradient. Main blue: #3978B8. Turquoise accent: #54C5C1. Dark navy text: #20344A. Large square a²: blue #3978B8. Both rectangles ab: identical turquoise #54C5C1. Small square b²: pale blue #BDD9EF, with navy text. Use matte surfaces and restrained highlights. Keep the background bright throughout. EXACT GEOMETRIC CONSTRUCTION Use positive lengths a and b, with a visually larger than b, approximately a:b = 3:2. The outer figure is a perfect square with side length a+b. Divide it with one vertical line and one horizontal line, both positioned at a distance a from the left and top edges. This produces exactly four regions: • Top-left: a × a square, area a². • Top-right: b × a rectangle, area ab. • Bottom-left: a × b rectangle, area ab. • Bottom-right: b × b square, area b². The two ab rectangles have equal areas and are rotated versions of each other. All four regions must fit together perfectly, without gaps or overlaps. ANIMATION TIMELINE 0–3 SECONDS — BUILD THE BIG SQUARE Show the short Azerbaijani title “Cəmin kvadratı” at the top. Two slim segments, one blue labelled “a” and one turquoise labelled “b”, join end to end. Their combined length becomes the top edge of a large square. Complete the square with a smooth line-drawing animation. Display a subtle dimension bracket labelled “a+b” above the square and another along its left side. Keep the square large and centered. 3–6 SECONDS — REVEAL THE FOUR AREAS Draw the internal vertical and horizontal dividing lines slowly and precisely. Fill the four regions with their assigned colors, one after another. Place small, readable labels in their centers: “a²”, “ab”, “ab”, “b²”. Keep all four pieces inside the original square during this reveal. The viewer should clearly see that the large square consists of these four areas. 6–10 SECONDS — MAKE THE TWO RECTANGLES CLEAR Move the four tiles slightly apart into an exploded view, preserving their original positions and orientations. Use only narrow, equal gaps. Briefly show “a” and “b” beside the edges of one turquoise rectangle. Gently highlight both turquoise rectangles at the same time to show that each has area ab. Below the figure, display the small expression “ab + ab = 2ab”. Connect each ab term to its corresponding turquoise rectangle with a thin, subtle line. Hold long enough to read. 10–13 SECONDS — REASSEMBLE Slide all four tiles smoothly back together into the perfect square. As each tile settles, briefly highlight its area label. The two ab rectangles settle together, reinforcing that there are TWO equal rectangular areas. Return the “a+b” side brackets. Keep the geometry visible and dominant. 13–15 SECONDS — FINAL VISUAL RESULT Hold the complete partitioned square on screen. Below it, reveal the equation in a single readable line: “(a+b)² = a² + 2ab + b²” Color the a² term blue, the 2ab term turquoise, and the b² term a darker blue matching the small square’s outline. Keep symbols and the left-hand side navy. The equation supports the visual proof; it must not replace or cover the figure. End with a calm, stable frame showing the four regions and the equation together. CAMERA, TEXT AND AUDIO Fixed, straight-on camera with a very subtle initial push-in. No rotation that distorts the square. Modern sans-serif typography with correct Azerbaijani characters and proper superscripts. Keep all important elements within the central safe area, away from the bottom and right-side social media controls. No narration. Use quiet ambient music and soft, understated sounds when tiles join. AVOID Dark backgrounds, neon colors, excessive glow, flashing, rapid cuts, decorative particles, unrelated objects, people, watermarks and invented logos. Do not change the proportions while tiles move. Do not turn the ab rectangles into squares. Do not omit either ab rectangle. Do not display “a²+b²” as the complete result. Prioritize accurate geometry, readable labels and smooth animation.