Explanation

t⁴ - 16 = (t²)² - 4² = (t² - 4)(t² + 4) = (t - 2)(t + 2)(t² + 4)

(t² + 4)(t + 2)(t - 2)

Last verified on 14-04-2026

Explanation

For x² - 4x + m to be a complete square, it must match (x - a)² = x² - 2ax + a²  

Compare: -2a = -4 → a = 2  

So m = a² = 2² = 4  

Check: x² - 4x + 4 = (x - 2)²  

Last verified on 14-04-2026

Explanation

Explanation

What are the factors ofx^2−5?

We use the identity:

a^2−b^2=(a−b)(a+b)

x^2−5=x^2− √5

(x − √5)(x + √5)

 Last updated NA 13-04-2026

Explanation

We are given:

$$(2a-7b,5b)=(-10a,3+b)$$

Step 1: Equate corresponding components

Since ordered pairs are equal:

1. First components:

$$2a-7b=-10a$$

2. Second components:

5b=3+b

Step 2: Solve second equation

5b=3+b
5b−b=3
$$4b=3$$

b=3/4​

Step 3: Substitute into the first equation

2a−7(3/4)=−10a
2a−21/4​=−10a

Bring like terms together:

$$2a + 10a = frac{21}{4}$$ $$12a = frac{21}{4}$$a=21​/48=7/16​

Final Answer:

a=7/16,b=3/4

 Last updated NA 13-04-2026
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Explanation

In the proportion 5 : 5 :: 6 : X, find X

We use the proportion rule:

$frac{a}{b} = frac{c}{d}$

Apply the values:

5/5​=6/X​
1=6/X​
$$X=6$$

$$Last\; updated\; NA\; 13-04-2026$$

Explanation

s² - 8s + 16 = 0  

Discriminant = b² - 4ac = (-8)² - 4(1)(16) = 64 - 64 = 0  

When D = 0, roots are Real and Equal.

Here: (s - 4)² = 0 → s = 4, 4  

Last verified on 12-04-2026

Explanation

Degree = sum of exponents on the variables.  

For 5x²yz: 2 + 1 + 1 = 4  

Last verified on 12-04-2026

Explanation

• An open sentence contains one or more variables (unknowns).
• Its truth value is not fixed (true or false).
• It becomes true or false only after substituting values.
• Closed sentence has no unknowns.
• Closed sentence always has fixed truth value.

Last verified on 11-04-2026

Explanation

Expand using distributive property (FOIL):

$$(x+3)(x-2)$$

x⋅x=x^2

x⋅(−2)=−2x

3⋅x=3x

3⋅(−2)=−6

Now combine like terms:

x^2−2x+3x−6=x^2+x−6