andLet’s find out the square of the expressions given below using the above identities –

i.

ii.

iii.

iv.

_{i. (5x – 2y)}²

_{Apply the formula (a-b)}² = a² + b² -2ab

_{Here a = 5x and b = 2y}

= (5x)² – 2(5x)(2y) + (2y)²

= 25x² – 20xy + 4y²

ii. (7 + 2m)²

Using, (a + b)² = a² + 2ab + b²

Here, a = 7, b = 2m

= (7)² + 2(7)(2m) + (2m)²

= 49 + 28m + 4m²

iii. (x + y + z)²

= (x + (y + z))²

Using, (a + b)² = a² + 2ab + b²

Here, a = x, b = y + z

= x² + 2(x)(y + z) + (y + z)²

Again, using, (a + b)² = a² + 2ab + b²

Here, a = y, b = z

= x² + 2xy + 2xz + y² + z² + 2yz

= x² + y² + z² + 2xy + 2yz + 2xz

iv. (a + b – c – d)²

= (a + b – (c + d))²

Using, (A - B)² = A² - 2AB + B²

Here, A = a + b, B = c + d

= (a + b)² – 2(a + b)(c + d) + (c + d)²

Using, (a + b)² = a² + 2ab + b²

= (a² + b² + 2ab) – 2(ac + ad + bc + bd) + (c² + d² + 2cd)

= a² + b² + c² + d² + 2ab – 2bc + 2cd – 2ad–2bd – 2ac