Вправи: 651

651. Спростіть вираз:

1) (x + 3)² + (x – 3)² = (x)² + 2 • x • 3 + 3² + (x)² – 2 • x • 3 + 3² = x + 6x + 9 + x – 6x + 9 = 2x + 18;

2) (a + 52)² – (a – 52)² = (a)² + 2a • 52 + (52)² – ((a)² – 2 • a • 52 + (52)²) = a + 102a + 50 – (a – 102a + 50) = a + 102a + 50 – a + 102a – 50 = 202a;

3) (2 + y)² – (1 – 2y)² = 2² + 2 • 2y + (y)² – (1² – 2 • 1 • 2y + (2y)²) = 4 + 4y + y – (1 – 4y + 4y) = 4 + 4y + y – 1 + 4y – 4y = 3 + 8y – 3y;

4) (x + 4)( x – 4) – (–x + 4)² = x – 4x + 4x – 16 = x – 16;

5) (m + n)² – (m + n)( m – n) = m + 2mn + n – (m – n) = m + 2mn + n – m + n = 2n + 2mn;

6) (x + y)(x – y) – (–x – y)² = x – y – (x + y)² = x – y – (x + 2xy + y) = x – y – x – 2xy – y = –2y – 2xy.