Question

1.

a) (x+3)^2=
b) (a-2)^2=
c) (2x+5)^ 2

2.

a) (x-1)(x^3 + x^2 + x +1)=
b) (x+1)(x^3-x^2+x-1)=

3.
a) (x+7)(2x-1)=
b) (2a-1)(a+4)=
c) ( 4a-1)(2-3a)=
d) (a^5-1)(a+1)=
e) (x^7-x^5)(x^3+x^2)=
f) (2k^2-1)(2k+1)=
g) (3-p^3)(p^2+1)=

4.

a) (x+√5)(x-√5)

b) (2y-3)(y+1)

c) (a+√2)(a-√3)

d) (2√2+k)(√2-k)

Answer 1

a) (x+3)^2= x² + 6x + 9

b) (a-2)^2= x² - 4x + 4
c) (2x+5)^ 2 = 4x² + 20x + 25

2.

a) (x-1)(x^3 + x^2 + x +1)= x⁴ + x³ + x² + x - x³ - x² - x - 1 = x⁴ -1
b) (x+1)(x^3-x^2+x-1)=x⁴ - x³ + x² - x + x³ - x² + x - 1 = x⁴ - 1

3.
a) (x+7)(2x-1)= 2x² - x + 17x - 7 = 2x² + 16x - 7
b) (2a-1)(a+4)= 2a² + 8a - a - 4 = 2a² + 7a - 4
c) ( 4a-1)(2-3a)= 8a - 12a² - 2 + 3a = 11a - 12a² - 2
d) (a^5-1)(a+1)=a⁶ + a⁵ - a + 1
e) (x^7-x^5)(x^3+x^2)=x¹⁰ + x¹⁴ - x⁸ - x⁷
f) (2k^2-1)(2k+1)= 4k³ + 2k² - 2k - 1
g) (3-p^3)(p^2+1)= 3p² + 3 - p⁵ - p³

4.

a) (x+√5)(x-√5) = x² - √5x + √5x - 5 = x² -5

b) (2y-3)(y+1) = 2y² + 2y - 3y - 3 = 2y² - y - 3

c) (a+√2)(a-√3) = a² - √3a + √2a - √6

d) (2√2+k)(√2-k) = 4 - 2√2k + √2k - k² = 4 - √2k - k²