Question

Use the identity (x + a) (x + b) = x² + (a + b) x + ab to find the value of the following product :(1) (x - 7) (x - 12)
(2) (5 - 4x) (7 — 4x)(3) (x + 3/2) (2x +5/3)
(4) (3x + 3/2) (3x + 5/2)

Answer 1

Answer:

Formula used:

$\bf{(x+a)(x+b)=x^2+(a+b)x+ab}$

$\text{1. (x-7)(x-12)}$

$=x^2+(-7-12)x+(-7)(-12)$

$=x^2-19x+84$

$\boxed{(x-7)(x-12)=x^2-19x+84}$

$\text{2. (5-4x)(7-4x)}$

$=(4x-5)(4x-7)$

$=(4x)^2+(-5-7)(4x)+(-5)(-7)$

$=16x^2-48x+35$

$\boxed{(5-4x)(7-4x)=16x^2-48x+35}$

$\text{3. (x+3/2)(2x +5/3)}$

$=\frac{1}{2}(2x+3)(2x+\frac{5}{3})$

$=\frac{1}{2}[(2x)^2+(3+\frac{5}{3})(2x)+(3)(\frac{5}{3})]$

$=\frac{1}{2}[4x^2+\frac{28}{3}x+5]$

$\boxed{(x+3/2)(2x +5/3)=\frac{1}{2}[4x^2+\frac{28}{3}x+5]}$

$\text{4. (3x + 3/2)(3x + 5/2)}$

$=(3x)^2+(\frac{3}{2}+\frac{5}{2})(3x)+(\frac{3}{2})(\frac{5}{2})$

$=9x^2+12x+\frac{15}{4}$

$\boxed{(3x + 3/2)(3x + 5/2)=9x^2+12x+\frac{15}{4}}$