Question

Bagi2 point
jabarkanlah setiap bentuk perkalian berikut dengan menggunakan skema!
•(2a-5)(2a+9)
•(15-4y)(15+4y)
•(9+12y)(9-12y)
•(x²+y²)(x²-y²)
•(x²+5x)(x²-10y
•(4x²-2y)(4x²-5y)
•(5x²-8x)(5x²+8)
jawab pake cara

Answer 1

Verified answer

Mapel : Matematika
Kelas : VII SMP
Bab : Aljabar dasar

Rumus dasar :
1. (a - b)(a + b) = a² - b²
2. (a + b)² = a² + 2ab + b²
3. (a - b)² = a² - 2ab + b²

Pembahasan :
(2a - 5)(2a + 9)
= (2a)(2a) + (2a)(9) + (-5)(2a) + (-5)(9)
= 4a² + 18a - 10a - 45
= 4a² + 8a - 45

(15 - 4y)(15 + 4y)
= 15² - (4y)² ——» Use Rumus 1
= 225 - 16y²

(9 + 12y)(9 - 12y)
= 9² - (12y)² ——» Use Rumus 1
= 81 - 144y²

(x² + y²)(x² - y²)
= (x²)² - (y²)²
= x⁴ - y⁴

(x² + 5x)(x² - 10y)
= (x²)² + (x²)(-10y) + (5x)(x²) + (5x)(-10y)
= x⁴ - 10x²y + 5x³ - 10xy

(4x² - 2y)(4x² - 5y)
= (4x²)² + (4x²)(-5y) + (-2y)(4x²) + (-2y)(-5y)
= 16x⁴ - 20x²y - 8x²y + 10y²
= 16x⁴- 28x²y + 10y²

(5x² - 8x)(5x² + 8)
= (5x²)² + (5x²)(8) + (-8x)(5x²) + (-8x)(8)
= 25x⁴ + 40x² - 40x³ - 64x²
= 25x⁴ - 40x³ - 16x²