How do you combine like terms in ${(2 a + 3)}^{2} + {(a - 5)}^{2}$ $(2a + 3) ^ { 2} + ( a - 5) ^ { 2}$ ?

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Answer 1 · 2018-06-09T18:42:42

$5 a^{2} + 2 a + 34$ $5a^2+2a+34$

Using the formulas

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $(a+b)^2=a^2+2ab+b^2$
${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ $(a-b)^2=a^2-2ab+b^2$
we get

$4 a^{2} + 9 + 12 a + a^{2} - 10 a + 25$ $4a^2+9+12a+a^2-10a+25$
and this is

$5 a^{2} + 2 a + 39$ $5a^2+2a+39$

Answer 2 · 2018-06-09T18:43:18

$5 a^{2} + 2 a + 34$ $5a^2+2a+34$

First FOIL the squared terms:

$= {(2 a + 3)}^{2} + {(a - 5)}^{2}$ $=(2a+3)^2+(a-5)^2$

$= (2 a + 3) (2 a + 3) + (a - 5) (a - 5)$ $=(2a+3)(2a+3)+(a-5)(a-5)$

$= 4 a^{2} + 6 a + 6 a + 9 + a^{2} - 5 a - 5 a + 25$ $=4a^2+6a+6a+9+a^2-5a-5a+25$

now "combine like terms":

$= 5 a^{2} + 2 a + 34$ $=5a^2+2a+34$

How do you combine like terms in (2a+3)2+(a−5)2(2a + 3) ^ { 2} + ( a - 5) ^ { 2}?