Use Identity 1A to find the values of $104^2, 37^2$. (Hint: Decompose 104 and 37 into sums or differences of numbers whose squares are easy to compute.) (Identity 1A $\quad(a+b)^2=a^2+2 a b+b^2$).
View full solution →Question types
We Distribute, Yet Things Multiply question types
15 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
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Sample Questions
We Distribute, Yet Things Multiply questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $a$ and $b$ are any two integers, is $(a+b)^2$ always greater than $a^2+b^2$ ? If not, when is it greater?
View full solution →Expand (i) $(a-b)(a+b)$, (ii) $(a-b)\left(a^2+a b+b^2\right)$, and (iii) $(a-b)\left(a^3+a^2 b+a b^2+b^3\right)$, Do you see a pattern? What would be the next identity in the pattern that you see? Can you check it by expanding?
View full solution →Observe the multiplication grid below. Each number inside the grid is formed by multiplying two numbers. If the middle number of a 3 × 3 frame is given by the expression pq, as shown in the figure, write the expressions for the other numbers in the grid.
Find 3 examples where the product of two numbers remains unchanged when one of them is increased by 2 and the other is decreased by 4.
Expand the following product.
(5 + z) (y + 9)
(5 + z) (y + 9)
Expand the following product.
(–5a + b) (c + d)
(–5a + b) (c + d)
Expand the following product.
(3 – x) (x – 6)
(3 – x) (x – 6)
Expand the following product.
(10a + b) (10c + d)
(10a + b) (10c + d)
Expand the following product.
2/3 (15 + 6a)
2/3 (15 + 6a)
Find the general expansion of $(a-b)^2$ using geometry, as we did for $55^2$.
View full solution →Expand $(3 j+2 k)^2$ using both the identity and by applying the distributive property.
View full solution →Use Identity 1A to write the expressions for the following.
(i) $(m+3)^2$
(ii) $(6+p)^2$
(Identity 1A $\quad(a+b)^2=a^2+2 a b+b^2$).
View full solution →(i) $(m+3)^2$
(ii) $(6+p)^2$
(Identity 1A $\quad(a+b)^2=a^2+2 a b+b^2$).
Expand (i) (a + ab – 3b2) (4 + b), and (ii) (4y + 7) (y + 11z – 3).
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