Polynomials Test - 11

(2z + 3x + 2) (-2x + 2 - 3z)
2z (-2x + 2 - 3z) + 3x (-2x + 2 - 3z) + 2 (-2x + 2 - 3z)
= -4xz + 4z - 6z² - 6x² + 6x - 9xz - 4x + 4 - 6z
= -6x² - 6z² - 13xz + 2x - 2z + 4

301 × 302 = (300 + 1)(300 + 2)
Use identity (x + a)(x + b) = x² + (a + b)x + ab.

Putting x = 300, a = 1 and b = 2 in the above equation, we get
90000 + (1 + 2)300 + 1 × 2

Now comparing it with the original equation given in the question, we get
m × n = 2

z(x - y) = a
x = 4, y = 1, z = 2
a = 2(4 - 1) = 2(3) = 6

(x² – 3) (x + 3) + 9
= x³ + 3x² – 3x – 9 + 9
= x³ + 3x² – 3x
= x(x² + 3x – 3)

2a + b = 45, b = 3
2a + 3 = 45
2a = 45 - 3
2a = 42
a = 42/2 = 21

3x – 7y = 10
Squaring both sides
9x² + 49y² - 42xy = 100
9x² + 49y² + 84 = 100 ( Given xy = -2)
9x² + 49y² = 16

(7x + 8y)² + (7x - 8y)²
= (7x)² + (8y)² + 2(7x)(8y) + (7x)² + 8y² - 2(7x)(8y)
= 49x² + 64y² + 49x² + 64y²
= 98x² + 128y²