20 Middle Term Splitting Questions with Solutions

To factorize this expression, we need to find two numbers α and β such that α + β = –12 and αβ = 36

4x² – 6x – 6x + 9

2x(x – 3) – 3(x – 3)

(2x – 3)(x – 3)

To factorize this expression, we need to find two numbers α and β such that α + β = –28 and αβ = 140

10y² – 14y – 10y + 14

2y(5y – 7) – 2(5y – 7)

(2y – 2)(5y – 7)

2(y – 1)(5y – 7)

To factorize this expression, we need to find two numbers α and β such that α + β = –10 and αβ = 25

x² – 5x – 5x + 25

x(x – 5) – 5(x – 5)

(x – 5)(x – 5)

(x – 5)²

To factorise the above equation, we need to find two numbers α and β such that α + β = 8 and αβ = 16 

y² + 4y + 2y + 16

y(y + 4) + 2(y + 4)

(y + 2)(y + 4)

To factorize this expression, we need to find two numbers α and β such that α + β = -4 and αβ = -12

z² – 6z + 2z – 12

z(z – 6) + 2(z – 6)

(z + 2)(z – 6)

To factorize this expression, we need to find two numbers α and β such that α + β = 34 and αβ = 225

25x² + 9x + 25x + 9

x(25x + 9) + 1(25x + 9)

(25x + 9)(x + 1)

To factorize this expression, we need to find two numbers α and β such that α + β = 2 and αβ = 1

x⁴ + x²y² + x²y² + y⁴

x²(x² + y²) + y²(x² + y²)

(x² + y²)(x² + y²)

(x² + y²)²

To factorize this expression, we need to find two numbers α and β such that α + β = 84 and αβ = 1764

49a² + 42ab + 42ab + 36b²

7a(7a + 6b) + 6b(7a + 6b)

(7a + 6b)(7a + 6b)

(7a + 6b)²

a² + b² + 2ab – 4ab

a²  + b² – 2ab

a² – ab + b² – ab

a(a –b) – b(a – b)

(a – b)(a – b)

(a – b)²

To factorize the expression 121x² – 88xy + 16y², we can look for two numbers α and β such that α + β = -88 and αβ = 16 * 121.

The numbers that satisfy these conditions are -44 and -44 (-44 + -44 = -88 and -44 * -44 = 16 * 121 = 1936).

121x² – 44xy – 44xy + 16y²

(121x² – 44xy) – (44xy – 16y²)

11x(11x – 4y) – 4y(11x – 4y)

(11x – 4y)(11x – 4y)

(11x – 4y)²

To factorize this expression, we need to find two numbers α and β such that α + β = -6 and αβ = 9

1 – 3x – 3x + 9x²

(1 – 3x) – 3x(1 – 3x)

(1 – 3x)(1 – 3x)

(1 – 3x)²

To factorize this expression, we need to find two numbers α and β such that α + β = 0.9 and αβ = 0.2

0.4x² + 0.4x + 0.5x + 0.5

0.4 x(x+1) + 0.5 (x+1)

(0.4x + 0.5)(x+1)

We need to find two numbers α and β such that α + β = -80 and αβ = 16 * 100.

To factorize the expression, we split the middle term -80xy into two terms: -64xy and -16xy.

100x² – 64xy – 16xy + 16y²

(100x² – 64xy) + (-16xy + 16y²)

4x(25x – 16y) – 16y(25x – 16y)

(25x – 16y)(4x – 16y)

To factorize this expression, we need to find two numbers α and β such that α + β = 5 and αβ = -14.

We can factorize the expression as follows:

x²y² – 2xyz + 7xyz – 14z²

(x²y² – 2xyz) + (7xyz – 14z²)

xy(xy – 2z) + 7z(xy – 2z)

(xy – 2z)(xy + 7z)

3(xy)² – (xy)(yz) – 24(yz)²

To factorize this expression, we need to find two numbers α and β such that α + β = 1 and αβ = 72

3(xy)² – 9(xy)(yz) + 8(xy)(yz) – 24(yz)²

3xy²(x – 3z) + 8y²z(x – 3z)

y²[3x(x – 3z) + 8z(x – 3z)]

y²(x – 3z)(3x + 8z)

y²(x – 3z)(3x + 8z)

To factorize this expression, we need to find two numbers α and β such that α + β = -6 and αβ = 9

11(a + b)² + 22(a+b)(c + d) – (a+b)(c + d) – 2(c + d)²

11(a + b)[(a+b) + 2(c + d)] – (c + d)[(a + b) + 2(c + d)]

(a + b + 2c + 2d)(11a + 11b – c – d)

Writing the above equation as:

x² + (2/x)² + 2 × x × (2/x)

Using the formula (a + b)² = a² + 2ab + b², we get

(x + 2/x)²

√3a² + 3a + 2a + 2√3

√3a(a + √3) + 2(a + √3)

(√3a + 2)(a + √3)

Rewriting the above equation as

(2x)² + 1/(4x)² + 2 × 2x × 1/4x

Using the formula (a + b)² = a² + 2ab + b², we get

(2x + 1/4x)²

Rewriting the above equation as

(s² + r² + 2sr) + 1/4(s + r)² + 2 × (s + r)² × 1/2(s + r)²

(s + r)² + 1/{2(s + r)²} + 2 × (s + r)² × 1/2(s + r)²

Using the formula (a + b)² = a² + 2ab + b², we get

{(s + r) + 1/2(s + r)}²