Question

Factorising using difference of two squares :

a) (x + 1)² - 25
&
b) 49 - (1 - x)²​

Answer 1

a) (x + 6)(x - 4)

Explanation:

a) (x+1)^2 - 25

=(x+1)(x+1) - 5 x 5

Remember the formula for a difference of two squares is

a^2 – b^2 = (a + b)(a – b) or (a – b)(a + b)

so a = x+1 and b = 5

therefore to factorise it would be

(x + 1 + 5)(x + 1 - 5)

= (x + 6)(x - 4)

b) For the next one, it's a similar:

root 49 is 7, and the equation (1 - x) has been squared so

a = 7 and b = - (1 - x)

The last part is the same as a), if you still need help, just ask me :)

Tip: don't forget to incorporate the negative, it's important!

Hope this helped,

Cate