Find the product of (2a + 3b) (2a + 3b) using identities

Mathematics

1 answer:

Step2247 [10]3 years ago

7 0

Answer:

4a^2 + 12ab + 9b^2.

Step-by-step explanation:

Use the identity (a + b)(a + b) = a^2 + 2ab + b^2 :

(2a + 3b)(2a + 3b)

= (2a)^2 + 2*(2a)(3b) + (3b)^2

= 4a^2 + 12ab + 9b^2.

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The ratio of the sides of 2 cubes is 2 to 7. If the volume of the smaller cube is 32 u3, then the volume of the larger cube is _

satela [25.4K]

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\$

$\bf \cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{2}{7}=\cfrac{\sqrt[3]{32}}{\sqrt[3]{v}}\implies \cfrac{2}{7}=\sqrt[3]{\cfrac{32}{v}}\implies \left( \cfrac{2}{7} \right)^3=\cfrac{32}{v}
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5 0

3 years ago

Solve the equation a/a^2-9 +3/a-3=1/a+3

MAXImum [283]

Answer is: a= -4
STEP
1
:

1
Simplify —————
a + 3
Equation at the end of step
1
:

a 3 1
(————————+—————)-——— = 0
((a2)-9) (a-3) a+3
STEP
2
:

3
Simplify —————
a - 3
Equation at the end of step
2
:

a 3 1
(————————+———)-——— = 0
((a2)-9) a-3 a+3
STEP
3
:

a
Simplify ——————
a2 - 9
Equation at the end of step
3
:

a 3 1
(————————————————— + —————) - ————— = 0
(a + 3) • (a - 3) a - 3 a + 3

Equation at the end of step
4
:

(4a + 9) 1
————————————————— - ————— = 0
(a + 3) • (a - 3) a + 3
Pull out like factors :

3a + 12 = 3 • (a + 4)

Equation at the end of step
6
:

3 • (a + 4)
————————————————— = 0
(a + 3) • (a - 3)

3•(a+4)
——————————— • (a+3)•(a-3) = 0 • (a+3)•(a-3)
(a+3)•(a-3)

a+4 = 0

Subtract 4 from both sides of the equation :
a = -4

7 0

3 years ago

I need the answer ASAP please

lara [203]

a $\leq$ 7