Answer:
5x+25
Step-by-step explanation:
A = l*w
We know the length is 5 and the width is (x+5)
A = 5*(x+5)
Distribute
A = 5x+25
<h3>4 times a number increased by 3.</h3>
When we have a number that appears
right before a variable, it means multiplication.
So 4n means the same thing as 4 times a number.
Remember, n is a variable which is just a
letter that represents any number.
Since we are adding 3 to 4n, we can say
4 times a number increased by 3.
So 4n + 3 can be written as 4 times a number increased by 3.
Answer:
Step-by-step explanation:1.1c
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<span><span> 8x24-27y6</span> </span>Final result :<span> (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
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Step by step solution :<span> Step 1 :</span>Skip Ad
<span>Equation at the end of step 1 :</span><span><span> (8 • (x24)) - 33y6
</span><span> Step 2 :</span></span><span>Equation at the end of step 2 :</span><span> 23x24 - 33y6
</span><span> Step 3 :</span>Trying to factor as a Difference of Squares :
<span> 3.1 </span> Factoring: <span> 8x24-27y6</span>
Theory : A difference of two perfect squares, <span> A2 - B2 </span>can be factored into <span> (A+B) • (A-B)
</span>Proof :<span> (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
<span> A2 - B2</span>
</span>Note : <span> AB = BA </span>is the commutative property of multiplication.
Note : <span> - AB + AB </span> equals zero and is therefore eliminated from the expression.
Check :<span> 8 is not a square !!
</span>Ruling : Binomial can not be factored as the
difference of two perfect squares
Trying to factor as a Difference of Cubes:
<span> 3.2 </span> Factoring: <span> 8x24-27y6</span>
Theory : A difference of two perfect cubes, <span> <span>a3</span> - <span>b3</span> </span> can be factored into
<span> (a-b) • (a2 +ab +b2)</span>
Proof : <span> (a-b)•(a2+ab+b2) =
<span>a3</span>+<span>a2b</span>+<span>ab2</span>-<span>ba2</span>-<span>b2a</span>-<span>b3</span> =
<span>a3</span>+(<span>a2b</span>-<span>ba2</span>)+(<span>ab2</span>-<span>b2a</span>)-<span>b3</span> =
<span>a3</span>+0+0+<span>b3</span> =
<span>a3</span>+<span>b3</span></span>
Check : 8 is the cube of 2
Check : 27 is the cube of 3
Check :<span> x24</span> is the cube of <span> x8</span>
Check :<span> y6</span> is the cube of <span> y2</span>
<span>Factorization is :
</span> <span> <span>(2x8 - 3y2)</span> • </span><span> (4x16 + 6x8y2 + 9y4)</span>
Trying to factor as a Difference of Squares :
<span> 3.3 </span> Factoring: <span> 2x8 - 3y2</span>
Check :<span> 2 is not a square !!
</span>Ruling : Binomial can not be factored as the
difference of two perfect squares
Trying to factor a multi variable polynomial :
<span> 3.4 </span> Factoring <span> 4x16 + 6x8y2 + 9y4</span>
Try to factor this multi-variable trinomial using trial and error<span>
</span>Factorization fails
Final result :<span> (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
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