Question

use suitable identitites to find the following products :
1.
$(x + 4)(x + 10)$
​

Answer 1

$\Large{\underbrace{\underline{\sf{Understanding\; The\; Question}}}}$

Here this is a question from algebric expressions, we have given an equation and we have to expand it using Identities. The following Identities are more frequently used:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textsbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\sf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\sf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\sf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\sf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\sf{9)(X+A)(X+B)=X^{2}+(A+B)X+AB}\\\end{minipage}}$

$\rule{350}{2}$

From here we can see that the following Identity matches the given equation:

(X+A)(X+B)=X²+(A+B)X+AB

Value of A will be 4 and B=10 according to given equation.

$\rule{350}{2}$

So by applying this identity we can expand the given term.

(X+4)(X+10)=X²+(4+10)X+(4)(10)

(X+4)(X+10)=X²+14X+40

So the final answer is X²+14X+40.

$\rule{350}{2}$

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