Question

Using the identities of algebraic expressions, Find the following

(i) (a + 9)(a + 9)

(ii) (1.9b + 1.1c)(1.9b - 1.1c)

(iii) (n - 4)(n - 4)

(iv)(-x + y)(-x + y) [4 MARKS]

Answer 1

Application: 1 Mark each

$\left(i\right)(a+9)(a+9)$

$={(a+9)}^2$

$={\left(a\right)}^2+{\left(9\right)}^2+2\left(a\right)\left(9\right)$

$=a^2+81+18a$


$\left(ii\right)(1.9b+1.1c)(1.9b-1.1c)$

$=(1.9b{)}^2-(1.1c{)}^2$

$=3.61b^2-{1.21c}^2$


$\left(iii\right)(n-4)(n-4)$

$={(n-4)}^2$

$={\left(n\right)}^2+{\left(4\right)}^2-2\left(n\right)\left(4\right)$

$={\left(n\right)}^2+16-8n$


$\left(iv\right)(-x+y)(-x+y)$

$={(y-x)}^2$

$={\left(y\right)}^2+{\left(x\right)}^2-2\left(x\right)\left(y\right)$

$={\left(y\right)}^2+{\left(x\right)}^2-2xy$