Simplify the following expressions: 4.2.2 (x+6)2 + (x−10)2 and 4.2.3 (x−3)(x+5)−(x−9)2.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to simplify the expressions:

4.2.2 $(x+6)^2 + (x-10)^2$

Expand the first term $(x+6)^2$ .
$(x+6)^2 = x^2 + 2(x)(6) + 6^2 = x^2 + 12x + 36 \quad (\text{Result 1})$
Expand the second term $(x-10)^2$ .
$(x-10)^2 = x^2 + 2(x)(-10) + (-10)^2 = x^2 - 20x + 100 \quad (\text{Result 2})$
Add Result 1 and Result 2.
$(x^2 + 12x + 36) + (x^2 - 20x + 100)$ $= x^2 + x^2 + 12x - 20x + 36 + 100$ $= \boxed{2x^2 - 8x + 136}$
4.2.3 $(x-3)(x+5)-(x-9)^2$
Use the answer from 4.1.1 for $(x-3)(x+5)$ .
From 4.1.1, we know that $(x-3)(x+5) = x^2 + 2x - 15 \quad (\text{Result A})$
Use the answer from 4.1.2 for $(x-9)^2$ .
From 4.1.2, we know that $(x-9)^2 = x^2 - 18x + 81 \quad (\text{Result B})$
Substitute Result A and Result B into the expression and simplify.
Remember to distribute the negative sign to all terms in Result B.
$(x^2 + 2x - 15) - (x^2 - 18x + 81)$ $= x^2 + 2x - 15 - x^2 + 18x - 81$ $= (x^2 - x^2) + (2x + 18x) + (-15 - 81)$ $= 0x^2 + 20x - 96$ $= \boxed{20x - 96}$

Simplify the following expressions: 4.2.2 (x+6)2 + (x-10)2 and 4.2.3 (x-3)(x+5)-(x-9)2.