Question

Find the product using the formula.

Answer 1

(1) (x + 3) (x + 7)

Using the identity (x + a) (x + b) = x² + (a + b) x + ab:

(x + 3) (x + 7) = x² + (3 + 7) x + 21

= x² + 10 x + 21

(2) (y + 3) (y + 5)

Using the identity (x + a) (x + b) = x² + (a + b) x + a b:

(y + 3) (y + 5) = y² + (3 + 5) x + 15

= y² + 8 y + 15

(3) (m + 4) (m + 5)

Using the identity (x + a) (x + b) = x² + (a + b) x + a b:

(m + 4) (m + 5) = m² + (4 + 5) m + 20

= m² + 9 m + 20

(4) (a + 10) (a + 5)

Using the identity (x + a) (x + b) = x² + (a + b) x + a b:

(a + 10) (a + 5) = a² + (10 + 5) a + 20

= m² + 15 m + 20

(5) (x + 8) (x + 2)

Using the identity (x + a) (x + b) = x² + (a + b) x + a b:

(x + 8) (x + 2) = x² + (8 + 2) x + 16

= x² + 10 x + 16

(6) (2a + 3) (2a − 7)

Using the identity (x + a) (x + b) = x² + (a + b) x + a b:

(2a + 3) (2a − 7) = 4a² + (3 − 7) 2a − 21

= 4a² − 8a − 21

(7) (2x − 5) (2x + 3)

Using the identity (x + a) (x + b) = x² + (a + b) x + a b:

(2x − 5) (2x + 3) = 4x² + (−5 + 3) 2x − 15

= 4x² − 4 x − 15

(8) (3x − 4) (3x + 8)

Using the identity (x + a) (x + b) = x² + (a + b) x + a b:

(3x − 4) (3x + 8) = (3x)² + (−4 + 8) 3x + (−4) × 8

= 9x² + 12 x − 32

(9) (a² − 3) (a² − 5)

Using the identity (x + a) (x + b) = x² + (a + b) x + ab:

(a² − 3) (a² − 5) = a⁴ + (−3 − 5) a² + (−3) × (−5)

= a⁴ − 8a² + 15

(10) (3p² + 1) (3p² + 4)

Using the identity (x + a) (x + b) = x² + (a + b) x + ab:

(3p² + 1) (3p² + 4) = (3p)⁴ + (1 + 4) 3p² + 1 × 4

= 9p⁴ + 15p² + 4