(a)This is a difference of two squares: a² − b² = (a−b)(a+b), with a=x, b=7.

(a)Find two numbers that multiply to 12 and add to 7: 3 and 4.

(a)Half of 6 is 3, so start with (x+3)². Expanding (x+3)² gives x²+6x+9, which is 4 more than the original expression, so subtract 4.

(a)Difference of two squares: a²−b² = (a−b)(a+b).

(a)Find factors of (2×3=6) that add to 7: 1 and 6. Split the middle term and factorise by grouping.

(a)Half of −4 is −2, so start with (x−2)². Expanding gives x²−4x+4, which is 5 more than the original, so subtract 5.

(a)Take out the common factor 3, then apply difference of squares to what remains.

(a)Find two numbers multiplying to 20 and adding to −9: −4 and −5.

(a)From (x−2)² − 5 = 0, (x−2)² = 5, so x − 2 = ±√5.

(a)Take out the common factor 5, then apply difference of two squares.