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chubhunter [2.5K]
3 years ago
9

Use the binomial squares pattern to multiply (7c²+6)²

Mathematics
1 answer:
SashulF [63]3 years ago
6 0

The solution is 49 c^{4}+84 c^{2}+36

Explanation:

The expression is \left(7 c^{2}+6\right)^{2}

The square of a binomial is always a trinomial.

To determine the square of a binomial we shall use the formula.

The formula to find the square of a binomial is

(a+b)^{2}=a^{2}+2 a b+b^{2}

Let us use this formula to multiply the expression \left(7 c^{2}+6\right)^{2}

Here a=7c^{2} and b=6

Substituting the values in the formula, we get,

\left(7 c^{2}+6\right)^{2}=\left(7 c^{2}\right)^{2}+2 \cdot 7 c^{2} \cdot 6+6^{2}

Squaring each term, we have,

\left(7 c^{2}+6\right)^{2}=49 c^{4}+2\cdot 7 c^{2} \cdot 6+36

Multiplying the product of two terms, we get,

\left(7 c^{2}+6\right)^{2}=49 c^{4}+84c^{2}+36

Thus, the solution is 49 c^{4}+84 c^{2}+36

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Step-by-step explanation:

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Find the approximate location of 2/3, 1/2, and 3/8 on a number line 0 to 1
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0.6 (terminating), 0.5, 0.375

Step-by-step explanation:

I would assume you are wanting these in decimal form. In that case, you would have:

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3 years ago
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What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi
Sphinxa [80]

Answer:

15,000\:\mathrm{mm^3}

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by V=s^2\cdot h, where s is the base length and h is the height. Substituting given values, we have: V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}

The volume of a trapezoidal prism is given by V=\frac{b_1+b_2}{2}\cdot l\cdot h, where b_1 and b_2 are bases of the trapezoid, l is the length of the height of the trapezoid and h is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (\frac{b_1+b_2}{2}) multiplied by the trapezoid's height (l).

Substituting given values, we get:

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Therefore, the total volume of the composite figure is 5,880+9,120=\boxed{15,000\:\mathrm{mm^3}} (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark

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