Question

Упростите выражение: 1) (a + 2)(a – 2) 2) (3b – 1)(3b + 1); 3) (a + 2b)(a – 2b); 4) (4a – b)(4a + b). 2) Разложите на множители: 1) 4x^2 – 1; 2) m^2 – a^2; 3) a^2 – 9y^2; 4) 49x^2 – 121a^2; 5) x^2y^2 – 1; 6) –a^4 + 16.

Answer 1

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Answer 2

1. (a + 2)(a – 2) = a^2 - 2a + 2a - 4 = a^2 - 4

2. (3b – 1)(3b + 1) = (3b)^2 - 1^2 = 9b^2 - 1

3. (a + 2b)(a – 2b) = a^2 - (2b)^2 = a^2 - 4b^2

4. (4a – b)(4a + b) = (4a)^2 - b^2 = 16a^2 - b^2

5. 4x^2 – 1 This expression cannot be factored further using real numbers.

6. m^2 – a^2 = (m + a)(m - a)

7. a^2 – 9y^2 = (a + 3y)(a - 3y)

8. 49x^2 – 121a^2 = (7x + 11a)(7x - 11a)

9. x^2y^2 – 1 = (xy + 1)(xy - 1)

10. –a^4 + 16 = -(a^2)^2 + 4^2 = (4 + a^2)(4 - a^2) = (4 + a^2)(2 + a)(2 - a)