Question

1) x²+ 6xy+9
2) y² + 18y +81
3) p² - 4q²
4) 27x³- 8y³
5)a³+ 64b³
6) y² - y -42
7) z²+ z - 56
8) 25x²- 64y²
9) p⁴ - q⁴
10) 16x² - 49y²​

Answer 1

Step-by-step explanation:

$1) {x}^{2} + 6xy + 9$

$= ( {x})^{2} + 2 \times x \times 3 + ( {3})^{2}$

$= ({x + 3})^{2}$

$2) {y}^{2} + 18y + 81$

$= ({y})^{2} + 2 \times y \times 9 + ( {9})^{2}$

$= ( {y + 9})^{2}$

$3) {p}^{2} - 4 {q}^{2}$

$= ( {p})^{2} - (2 {q})^{2}$

$= (p + 2q)(p - 2q)$

$8)25 {x}^{2} - 64 {y}^{2}$

$= ( {5x})^{2} - ( {8y})^{2}$

$= (5x + 8y)(5x - 8y)$

$10)16 {x}^{2} - 49 {y}^{2}$

$= (4 {x})^{2} - (7 {y})^{2}$

$= (4x + 7y)(4x - 7y)$